Question

The tangent to the curve $y=x^2+3x$ will pass through the point $(0,-9)$ if it is drawn at the point

• A. $(0,1)$
• B. $(-3,0)$
• C. $(-4,4)$
• D. $(1,4)$

Answer 1

Answer: (B)

Equation of tangent at the point $(x,y)$ is
$Y-y=(2x+3)(X-x)$
If it passes through $(0,-9)$, then
$-9-y=(2x+3)(0-x)$
$\Rightarrow$ $y+9=2x^2+3x$
$\Rightarrow$ $x^2+3x+9=2x^2+3x$
$\Rightarrow$ $x^2=9$
$\Rightarrow$ $x=\pm 3$
$\therefore$ $y=18$ or $0$.
$\therefore$ $(-3,0)$ is the choice out of given points.