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Prove that the tangents drawn on the par...

Prove that the tangents drawn on the parabola `y^(2)=4ax`at points x = a intersect at right angle.

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The angle between the tangents to the parabola y^(2)=4ax at the points where it intersects with the line x-y-a= 0 is

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The angle between tangents to the parabola y^2=4ax at the points where it intersects with teine x-y-a = 0 is (a> 0)

The locus of point of intersection of two normals drawn to the parabola y^2 = 4ax which are at right angles is

For what values of 'a' will the tangents drawn to the parabola y^2 = 4ax from a point, not on the y-axis, will be normal to the parabola x^2 = 4y.

Double ordinate A B of the parabola y^2=4a x subtends an angle pi/2 at the vertex of the parabola. Then the tangents drawn to the parabola at A .and B will intersect at (a) (-4a ,0) (b) (-2a ,0) (-3a ,0) (d) none of these

Prove that the locus of the poles of tangents to the parabola y^2=4ax with respect to the circle x^2+y^2=2ax is the circle x^2+y^2=ax .

Find the equations of the normals at the ends of the latus- rectum of the parabola y^2= 4ax. Also prove that they are at right angles on the axis of the parabola.

Consider the parabola whose focus is at (0,0) and tangent at vertex is x-y+1=0 Tangents drawn to the parabola at the extremities of the chord 3x+2y=0 intersect at what angle ?

Prove that the portion of the tangent intercepted,between the point of contact and the directrix of the parabola y^(2)= 4ax subtends a right angle at its focus.

NAGEEN PRAKASHAN ENGLISH-APPLICATIONS OF DERIVATIVES-Exercise 6d
  1. Find the equation of tangent of the curve 9x^(2)+16y^(2) = 144 at thos...

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  2. Find the co-ordinates of that point on the curve x^(3)+y^(3)= a^(3) a...

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  3. Find the co-ordinates of that point on the curvey^(2)=x^(2)(1-x) at wh...

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  4. Find the co-ordinates of that point on the curve x^(2)/a^(2)+y^(2)/b^(...

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  5. Prove that the equation of tangent of the ellipse x^(2)/a^(2)+y^(2)/b^...

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  6. Find the value of n in N such that the curve ((x)/(a))^(n)+((y)/(b))^(...

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  7. Show that the line x/a+y/b=1, touches the curve y=b.e^(-x//a) at the p...

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  8. Find the point on the curve y^(2) = x at which the tangent drawn makes...

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  9. Find the coordinates of the points on the curve y=x^2+3x+4, the tangen...

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  10. The tangent drawn at any point of the curve sqrtx+sqrty = sqrta meets...

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  11. If p and q are the intercept on the axis cut by the tangent of sqrt((x...

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  12. If tangents are drawn from the origin to the curve y=sin x , th...

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  13. Find the angle of intersection of the curves xy=a^(2)and x^(2)+y^(2)=2...

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  14. Prove that the curvesx^(2)-y^(2)=16 and xy = 15 intersect each other a...

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  15. Show that the condition that the curves ax^(2)+by^(2)=1anda'x^(2)+b'y^...

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  16. Prove that the curves "x"="y"^2 and "x y"="k" intersect at right ang...

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  17. Find the equations of the tangent and the normal at the point ' t ' ...

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  18. Prove that all the points of the curve y^(2)=4 alpha (x+a sin (x)/(a))...

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  19. Prove that the tangents drawn on the parabola y^(2)=4axat points x = a...

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  20. Prove that the curve y^2=4x and x^2 +y^2 - 6x +1=0 touches each other ...

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