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Statement 1: If the parabola y^2=4a x an...

Statement 1: If the parabola `y^2=4a x` and the circle `x^2+y^2+2b x=0` touch each other externally, then the roots of the equation `f(x)=x^2-(b+a+1)x+a=0` are real.
Statement 2: For parabola and circle touching externally, `a` and `b` must have the same sign.
(a) Statement 1 and Statement 2 are correct. Statement 2 is the correct explanation for the Statement 1.
(b) Statement 1 and Statement 2 are correct. Statement 2 is not the correct explanation for the Statement 1.
(c) Statement 1 is true but Statement 2 is false.
(d) Statement 2 is true but Statement 1 is false.

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Statement 1: There are no common tangents between the circle x^2+y^2-4x+3=0 and the parabola y^2=2xdot Statement 2:Given circle and parabola do not intersect. (a) Statement 1 and Statement 2 are correct. Statement 2 is the correct explanation for the Statement 1. (b) Statement 1 and Statement 2 are correct. Statement 2 is not the correct explanation for the Statement 1. (c) Statement 1 is true but Statement 2 is false. (d) Statement 2 is true but Statement 1 is false.

Statement 1: The line x-y-5=0 cannot be normal to the parabola (5x-15)^2+(5y+10)^2=(3x-4y+2)^2dot Statement 2: Normal to parabola never passes through its focus. (a) Statement 1 and Statement 2 are correct. Statement 2 is the correct explanation for the Statement 1. (b) Statement 1 and Statement 2 are correct. Statement 2 is not the correct explanation for the Statement 1. (c) Statement 1 is true but Statement 2 is false. (d) Statement 2 is true but Statement 1 is false.

Statement 1 : The number of circles passing through (1, 2), (4, 8) and (0, 0) is one. Statement 2 : Every triangle has one circumcircle (a) Statement 1 and Statement 2 are correct. Statement 2 is the correct explanation for the Statement 1. (b) Statement 1 and Statement 2 are correct. Statement 2 is not the correct explanation for the Statement 1. (c) Statement 1 is true but Statement 2 is false. (d) Statement 2 is true but Statement 1 is false.

Statement 1 : The number of circles touching lines x+y=1,2x-y=5, and 3x+5y-1=0 is four Statement 2 : In any triangle, four circles can be drawn touching all the three sides of the triangle. (a) Statement 1 and Statement 2 are correct. Statement 2 is the correct explanation for the Statement 1 (b) Statement 1 and Statement 2 are correct. Statement 2 is not the correct explanation for the Statement 1 (c) Statement 1 is true but Statement 2 is false (d) Statement 2 is true but Statement 1 is false

Statement 1: The normals at the points (4, 4) and (1/4,-1) of the parabola y^2=4x are perpendicular. Statement 2: The tangents to the parabola at the end of a focal chord are perpendicular. (a) Statement 1 and Statement 2 are correct. Statement 2 is the correct explanation for the Statement 1. (b) Statement 1 and Statement 2 are correct. Statement 2 is not the correct explanation for the Statement 1. (c) Statement 1 is true but Statement 2 is false. (d) Statement 2 is true but Statement 1 is false.

Statement 1 : Circles x^2+y^2=144 and x^2+y^2-6x-8y=0 do not have any common tangent. Statement 2 : If two circles are concentric, then they do not have common tangents. (a) Statement 1 and Statement 2 are correct. Statement 2 is the correct explanation for the Statement 1 (b) Statement 1 and Statement 2 are correct. Statement 2 is not the correct explanation for the Statement 1 (c) Statement 1 is true but Statement 2 is false (d) Statement 2 is true but Statement 1 is false

Statement 1: ""^m C_r+ ""^m C_(r-1)(""^nC_1)+ ""^mC_(r-2)(""^n C_2)+....+ ""^n C_r=0 , if m+n lt r Statement 2: ""^n C_r=0 , if n lt r (a) Statement 1 and Statement 2, both are correct. Statement 2 is the correct explanation for Statement 1. (b) Statement 1 and Statement 2, both are correct. Statement 2 is not the correct explanation for Statement 1. (c) Statement 1 is true but Statement 2 is false. (d) Statement 2 is true but Statement 1 is false.

Statement 1: Through (lambda,lambda+1) , there cannot be more than one normal to the parabola y^2=4x , if lambda (a) Statement 1 and Statement 2 , both are correct. Statement 2 is correct explanation for Statement 1. (b) Statement 1 and Statement 2 , both are correct. Statement 2 is not the correct explanation for Statement 1. (c) Statement 1 is correct but Statement 2 is not correct. (d) Statement 2 is correct but Statement 1 is not correct.

Statement 1: The circumcircle of a triangle formed by the lines x=0,x+y+1=0 and x-y+1=0 also passes through the point (1, 0). Statement 2: The circumcircle of a triangle formed by three tangents of a parabola passes through its focus. (a) Statement 1 and Statement 2 are correct. Statement 2 is the correct explanation for the Statement 1. (b) Statement 1 and Statement 2 are correct. Statement 2 is not the correct explanation for the Statement 1. (c) Statement 1 is true but Statement 2 is false. (d) Statement 2 is true but Statement 1 is false.

Statement 1: Each point on the line y-x+12=0 is equidistant from the lines 4y+3x-12=0,3y+4x-24=0 Statement 2: The locus of a point which is equidistant from two given lines is the angular bisector of the two lines. (a) Statement 1 and Statement 2 are correct. Statement 2 is the correct explanation for the Statement 1 (b) Statement 1 and Statement 2 are correct. Statement 2 is not the correct explanation for the Statement 1 (c) Statement 1 is true but Statement 2 is false (d) Statement 2 is true but Statement 1 is false

CENGAGE PUBLICATION-CONIC SECTIONS-All Questions
  1. Tangent is drawn at any point (x1, y1) other than the vertex on the pa...

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  2. The angle between the tangents to the curve y=x^2-5x+6 at the point (2...

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  3. Statement 1: If the parabola y^2=4a x and the circle x^2+y^2+2b x=0 to...

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  4. If a line y=3x+1 cuts the parabola x^2-4x-4y+20=0 at A and B , then th...

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  5. P(x , y) is a variable point on the parabola y^2=4a x and Q(x+c ,y+c) ...

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  6. If a and c are the lengths of segments of any focal chord of the parab...

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  7. AB is a chord the parabola y^(2)=4ax with vertex A. BC is drawn perpen...

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  8. Set of value of alpha for which the point (alpha,1) lies inside the ci...

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  9. If P is a point on the parabola y^(2)=3(2x-3) and M is the foot perpen...

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  10. If y=m x+c touches the parabola y^2=4a(x+a), then (a)c=a/m (b) c=a m...

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  11. The angle between the tangents to the paranola y^(2)=4ax at the points...

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  12. The area of the triangle formed by the tangent and the normal to the ...

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  13. Double ordinate A B of the parabola y^2=4a x subtends an angle pi/2 at...

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  14. Statement 1: The normals at the points (4, 4) and (1/4,-1) of the para...

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  15. Let A and B two distinct points on the parabola y^(2)=4x. If the axis ...

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  16. The equations of the common tangents to the parabola y = x^2 and y=-...

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  17. Let (x,y) be any point on the parabola y^2 = 4x. Let P be the point t...

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  18. The common tangents to the circle x^2 + y^2 =2 and the parabola y^2 = ...

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  19. If two distinct chords of a parabola y^2=4ax , passing through (a,2a) ...

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  20. The point of intersection of the tangents of the parabola y^(2)=4x dra...

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