Ellipse · Mathematics · TS EAMCET

If the focus of an ellipse is $(-1,-1)$, equation of its directrix corresponding to this focus is $x+y+1=0$ and its eccentricity is $\frac{1}{\sqrt{2}}$, then the length of its major axis is

If the normal drawn at the point $(2,-1)$ to the ellipse $x^{2}+4 y^{i}=8$ meets the ellipse again at $(a, b)$, then $17 a=$

If the locus of the centroid of the triangle with vertices $A(a, 0), B(a \cos t, a \sin t)$ and $C(b \sin ,-b \cos t)$ ( $t$ is a parameter) is $9 x^{2}+9 y^{2}-6 x \overline{\bar{x}} 49$, then the area of the triangle formed by the line $\frac{x}{a}+\frac{y}{b}=1$ with the coordinate axes is

$S=(-1,1)$ is the focus, $2 x-3 y+1=0$ is the directrix corresponding, to $S$ and $\frac{1}{2}$ is the eccentricity of an ellipse, If $(a, b)$ is the centre of the ellipse, then $3 a+2 b$ :

$a$ and $b$ are the semi-major and semi-minor axes of an ellipse whose axes are along the coordinate axes, If its latus rectum is of length 4 units and the distance between its foci is $4 \sqrt{2}$, then $a^{2}+b^{2}=$

If the extremities of the latus recta having positive ordinate of the ellipse $\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1(a > b)$ lie on the parabola $x^{2}+2 a y-4=0$, then the points $(a, b)$ lie on the curve

The length of the latus rectum of the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1(a>b)$ is $\frac{8}{3}$. If the distance from the centre of the ellipse to its focus is $\sqrt{5}$, then $\sqrt{a^2+6 a b+b^2}=$

$S$ is the focus of the ellips $\frac{x^2}{25}+\frac{y^2}{b^2}=1,(b<5)$ lying on the negative $X$-axis and $P(\theta)$ is a point on this ellipes. If the distance between the foci of this ellipse is 8 and $S^{\prime} P=7$, then $\theta=$

The equations of the directrices of the elmpse $9 x^2+4 y^2-18 x-16 y-11=0$ are

$L_1^{\prime}$ is the end of a latus rectum of the ellipse $3x=2 \pm \frac{\sqrt{5}}{\sqrt{5}}$ $3 x^2+4 y^2=12$ which is lying in the third quadrant. If the normal drawn at $L_1^{\prime}$ to this ellipse intersects the ellipse again at the point $P(a, b)$, then $a=$

If $6 x-5 y-20=0$ is a normal to the ellipse $x^2+3 y^2=K$, then $K=$