Question

The number of real tangents that can be drawn to the ellipse $3x^2+5y^2=32$ and $25x^2+9y^2=450$ passing through $(3,5)$ is

• A. $0$
• B. $2$
• C. $3$
• D. $4$

Answer 1

The correct option is C $3$

Since $3\times 3^2+5\times 5^2-32>0$, the point $(3,5)$ lies outside the ellipse

$3x^2+5y^2=32$.

Also, $25\times 3^2+9\times 5^2-450=0$

$\therefore$ the point $(3,5)$ lies on the ellipse $25x^2+9y^2=450$.

So the required number of tangents is $3$.