Home
Class 12
MATHS
The line2px+ysqrt(1-p^(2))=1(abs(p)lt1) ...

The line`2px+ysqrt(1-p^(2))=1(abs(p)lt1)` for different values of p, touches a fixed ellipse whose exes are the coordinate axes. Q. The locus of the point of intersection of prependicular tangents of the ellipse is

A

`x^(2)+y^(2)=2`

B

`x^(2)+y^(2)=3/2`

C

`x^(2)+y^(2)=5/4`

D

`x^(2)+y^(2)=1/2`

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • ELLIPSE

    ARIHANT MATHS|Exercise Exercise (Single Integer Answer Type Questions)|9 Videos

  • ELLIPSE

    ARIHANT MATHS|Exercise Ellipse Exercise 5: Matching Type Questions|3 Videos

  • ELLIPSE

    ARIHANT MATHS|Exercise Exercise (More Than One Correct Option Type Questions)|15 Videos

  • DY / DX AS A RATE MEASURER AND TANGENTS, NORMALS

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|7 Videos

  • ESSENTIAL MATHEMATICAL TOOLS

    ARIHANT MATHS|Exercise Exercise (Single Integer Answer Type Questions)|3 Videos

Similar Questions

Explore conceptually related problems

The line 2px+ysqrt(1-p^(2))=1(abs(p)lt1) for different values of p, touches a fixed ellipse whose exes are the coordinate axes. Q. The eccentricity of the ellipse is

The locus of the point of intersection of two prependicular tangents of the ellipse x^(2)/9+y^(2)/4=1 is

For all real p, the line 2px+ysqrt(1-p^(2))=1 touches a fixed ellipse whose axex are the coordinate axes The foci of the ellipse are

The ordinates of points P and Q on the parabola y^2 = 12x are in the ratio 1 : 2. Find the locus of the point of intersection of the normals to the parabola at P and Q.

A conic C satisfies the differential equation (1+y^(2))dx-xydy=0 and passes through the point (1, 0) . An ellipse E which is confocal with C having its eccentricity equal to sqrt((2)/(3)) Q. find the locus of the point of intersection of the perpendicular tangents to the ellipse E

Statement 1 The equation of the director circle to the ellipse 4x^(2)+9y^(2)=36 is x^(2)+y^(2)=13 Statement 2 The locus of the point of intersection of perpendicular tangents to an ellipse is called the director circle.

The locus of the middle point of the portion of a tangent to the ellipse x^2/a^2+y^2/b^2=1 included between axes is

Any ordinate MP of an ellipse meets the auxillary circle in Q. Ptove that the locus of the point of intersection of the normals at P and Q is the circle x^(2)+y^(2)=(a+b)^(2) .

A circle has the same center as an ellipse and passes through the foci F_1a n dF_2 of the ellipse, such that the two curves intersect at four points. Let P be any one of their point of intersection. If the major axis of the ellipse is 17 and the area of triangle P F_1F_2 is 30, then the distance between the foci is

Let P be the point (1,0) and Q be a point on the locus y^(2)=8x . The locus of the midpoint of PQ is