The locus of the point of intersection of two | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) The locus of the point of intersection of two perpendicular tangents to an ellipse is known as its director circle.The equation of the director ci

Vedclass · Accepted Answer

$x^2 + y^2 = 13$

Vedclass · Answer

(C) The locus of the point of intersection of two perpendicular tangents to an ellipse is known as its director circle.The equation of the director circle for an ellipse $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$ is given by $x^2 + y^2 = a^2 + b^2$.Given the ellipse $\frac{x^2}{9} + \frac{y^2}{4} = 1$,we have $a^2 = 9$ and $b^2 = 4$.Substituting these values into the equation,we get $x^2 + y^2 = 9 + 4$,which simplifies to $x^2 + y^2 = 13$.

The locus of the point of intersection of two perpendicular tangents to the ellipse $\frac{x^2}{9} + \frac{y^2}{4} = 1$ is:

Similar Questions

An arch is in the form of a semi-ellipse. It is $8 \, m$ wide and $2 \, m$ high at the centre. Find the height of the arch at a point $1.5 \, m$ from one end. (in $, m$)

If the straight line $8x + 3\sqrt{2}y = 36$ touches the ellipse $\frac{x^2}{9} + \frac{y^2}{4} = 2$ at $(a, b)$,then $a + \sqrt{2}b =$

If the eccentricity of an ellipse is $1/\sqrt{2}$,then its latus rectum is equal to its

If $4x - 3y + k = 0$ touches the ellipse $5x^{2} + 9y^{2} = 45$,then $k$ is equal to

The equations $x = a \cos \theta$ and $y = b \sin \theta$ with $a > b$ represent a conic section. Its eccentricity $e$ is given by:

Vedclass Test Series

Exam Paper Generator

Online Exam Module