$S_{1}$ and $S_{2}$ are the foci of an ellipse of major axis of length 10 units, and P is any point on the ellipse such that the perimeter or triangle $PS_{1}S_{2}$ is 15. Then the eccentricity of the ellipse is

$16x² + 25y² = 400.$

The locus of point of intersection $P$ of tangents to ellipse $2x^{2}+3y^{2}=6$ at $A$ and $B$ if $AB$ subtend $90^{o}$ angle at centre of ellipse is an ellipse whose eccentricity is equal to 

(i) $\mathrm{p}(\mathrm{x}+4)^{2}+\mathrm{q}(\mathrm{y}+1)^{2}=\mathrm{pq}$

(ii) $18 x^{2}+5 y^{2}=180$

দুইটি কণিক নির্দেশ করে ।

দৃশ্যকল্প: $f(x, y)=4 x^{2}+5 y^{2}-16 x+10 y+1$

$g(x)=a x^{2}+b x+c$