Dr. SK Goyal Solutions for Chapter: Ellipse, Exercise 3: INTRODUCTORY EXERCISE 6.3

From the point $\left(\lambda ,3\right)$ tangents are drawn to $\frac{x^2}{9}+\frac{y^2}{4}=1$ and are perpendicular to each other than $\lambda$ is :

The eccentric angle of one end of a diameter of $x^2+3y^2=3$ is $\pi /6$, then the eccentric angle of the other end will be :

The locus of the mid-points of a focal chord of the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ is :

The centre of the ellipse $\frac{{\left(x+y-2\right)}^2}{9}+\frac{{\left(x-y\right)}^2}{16}=1$ is :

The area of the parallelogram inscribed in the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ whose diagonals are the conjugate diameters of the ellipse is given by :

Find the locus of the mid-point of chords of the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1\left(a>b\right)$ passing through the point $\left(2a,0\right)$.

Obtain the locus of poles of tangents to the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ with respect to concentric ellipse $\frac{x^2}{{\alpha }^2}+\frac{y^2}{{\beta }^2}=1$.

Find the centre and eccentricity of the ellipse. $4{\left(x-2y+1\right)}^2+9{\left(2x+y+2\right)}^2=5$.