Question

The equation of tangent to the conic $S\equiv a{x}^2+b{y}^2+2hxy+2gx+2fy+c=0at(x_1,y_1)$ is obtained by replacing x with $\frac{x+x_1}{2},ywith\frac{y+y_1}{2},$with $x^2$ with $x{x}_1,y^2$ with $y{y}_1,xy$ with $\frac{x{y}_1+y{x}_1}{2}$ and keeping c as it is in the equation of conic (S).

• A. True
• B. False

Answer 1

The correct option is A

True

This is a standard result we discussed in circle. We recommend you to remember the method. It is helpful while finding the equation of tangent to any second degree curve. In this method replace $x$ with $\frac{x+x_1}{2}$,

$y\to \frac{y+y_1}{2}$

$x^2\to x{x}_1$

$y^2\to y{y}_1$

and

$c\to c$