Home
Class 12
MATHS
Statement 1 : If from any point P(x1, y1...

Statement 1 : If from any point `P(x_1, y_1)` on the hyperbola `(x^2)/(a^2)-(y^2)/(b^2)=-1` , tangents are drawn to the hyperbola `(x^2)/(a^2)-(y^2)/(b^2)=1,` then the corresponding chord of contact lies on an other branch of the hyperbola `(x^2)/(a^2)-(y^2)/(b^2)=-1`

Statement 2 : From any point outside the hyperbola, two tangents can be drawn to the hyperbola.

(a) Statement 1 and Statement 2 are correct and Statement 2 is the correct explanation for Statement 1.
(b) Statement 1 and Statement 2 are correct and 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.

Text Solution

Verified by Experts

Chord of contact of `(x^(2))/(a^(2))-(y^(2))/(b^(2))=1` w.r.t. point `P(x_(1),y_(1))` is
`(x x_(1))/(a^(2))-(yy_(1))/(b^(2))=1" (1)"`
Eq. (1) can be written as `(x(-x_(1)))/(a^(2))-(y(-y_(1)))/(b^(2))=-1`, which is tengent to the hyperbola `(x^(2))/(a^(2))-(y^(2))/(b^(2))=-1` at point `(-x_(1),-y_(1))`.
Obviously, points `(x_(1),y_(1)) and (-x_(1),-y_(1))` lie on the different branches of hyperbola `(x^(2))/(a^(2))-(y^(2))/(b^(2))=-1`.
Promotional Banner

Topper's Solved these Questions

  • HYPERBOLA

    CENGAGE PUBLICATION|Exercise CONCEPT APPLICATION EXERCISE 7.4|5 Videos

  • HYPERBOLA

    CENGAGE PUBLICATION|Exercise CONCEPT APPLICATION EXERCISE 7.5|5 Videos

  • HYPERBOLA

    CENGAGE PUBLICATION|Exercise CONCEPT APPLICATION EXERCISE 7.2|12 Videos

  • HIGHT AND DISTANCE

    CENGAGE PUBLICATION|Exercise Archives|3 Videos

  • INDEFINITE INTEGRATION

    CENGAGE PUBLICATION|Exercise Multiple Correct Answer Type|2 Videos

Similar Questions

Explore conceptually related problems

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 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: 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 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: 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 : 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 I The chord of contact of tangent from three points A, B and C to the circle x^2+y^2=a^2 are concurrent, then A, B and C will be collinear. Statement II A, B and C always lie on the normal to the circle x^2+y^2=a^2 . (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

Statement 1 :The circles x^2+y^2+2p x+r=0 and x^2+y^2+2q y+r=0 touch if 1/(p^2)+1/(q^2)=1/r Statement 2 : Two centers C_1a n dC_2 and radii r_1a n dr_2, respectively, touch each other if |r_1+r_2|=c_1c_2 (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 : Slopes of tangents drawn from (4, 10) to the parabola y^2=9x are and 1/4 and 9/4 . Statement 2 : Two tangents can be drawn to a parabola from any point lying outside the parabola. (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.