Question

Equation of a straight line through the point $(2,3)$ and perpendicular to straight line $4x+7y=9$ is :

• A. $7x+4y=26$
• B. $7x-4y+2=0$
• C. $\sqrt{7}x-4y=2$
• D. $noneofthese$

Answer 1

The correct option is C $\sqrt{7}x-4y=2$

$E{q}^n$ is $4x+7y=9$

$\Rightarrow 7y=9-4x$

Point is (2,3)

$\Rightarrow y=\frac{-4}{7}x+\frac{9}{7}$

Comparing with $y=mx+c,m=\frac{-4}{7}$

We know, that if lines are $\perp$ then $m_1\times m_2=-1$

$\Rightarrow m_2=\frac{7}{4}$

$\because (y-y_1)=(x-x_1)m$

$\Rightarrow (y-3)-\frac{7}{4}(x-2)$

$\Rightarrow 4y-12=7x-14$

$\sqrt{7x}-4y=2$