P is any point on the ellipse $9{x^2} + 36{y^2} = 324$, whose foci are $S$ and $S’$. Then $SP + S'P$ equals
$3$
$12$
$36$
$324$
(b) $SP + S'P = 2a$$ = 2.6 = 12$.
If the length of the latus rectum of the ellipse $x^{2}+$ $4 y^{2}+2 x+8 y-\lambda=0$ is $4$ , and $l$ is the length of its major axis, then $\lambda+l$ is equal to$……$
An ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1, a>b$ and the parabola $x^2=4(y+b)$ are such that the two foci of the ellipse and the end points of the latusrectum of parabola are the vertices of a square. The eccentricity of the ellipse is
If the variable line $y = kx + 2h$ is tangent to an ellipse $2x^2 + 3y^2 = 6$ , the locus of $P (h, k)$ is a conic $C$ whose eccentricity equals
A tangent having slope of $-\frac{4}{3}$ to the ellipse $\frac{{{x^2}}}{{18}}$ + $\frac{{{y^2}}}{{32}}$ $= 1$ intersects the major and minor axes in points $A$ and $ B$ respectively. If $C$ is the centre of the ellipse then the area of the triangle $ ABC$ is : ………….. $\mathrm{sq. \,units}$
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