Question

Tangents are drawn to the ellipse $3x^2+5y^2=32$ and $25x^2+9y^2=450$ passing through the point $(3,5)$. Then the number of such tangents are

• A. $2$
• B. $3$
• C. $4$
• D. $0$

Answer 1

The correct option is B $3$

Putting (3, 5) in the equation of the ellipse, we get $S_1=+ive$ and $S_2=0$ so that the point (3, 5) lies outside $S_1=0$ and hence two tangents can be drawn through the point (3, 5). The point (3, 5) lies on $S_2=0$ and only one tangent can be drawn. Thus the total no. of tangents passing through (3, 5 ) to the two ellipses is $2+1=3\Rightarrow \left(b\right).$
Ans: 3