Explanation

(c)
Let $S_{1} = 3x^{2} + 5y^{2} - 32$
and $S_{2} = 25x^{2} + 9y^{2} - 450$
[image:11_image78.emf]
At point (3, 5)
$S_{1} = 3(3)^{2} + 5(5)^{2} - 32 = 120 > 0$
and $S_{2} = 25(3)^{2} + 9(5)^{2} - 450$
$= 225 + 225 - 450 = 0$
$\therefore$ Point $(3,\ 5)$ lies outside the first ellipse and for second$\$ellipse lies on the ellipse.
Hence, two tangents for first ellipse and one tangent for second ellipse can be drawn