Question

Assertion :The product of the perpendiculars from the point $(1,3)$ on the lines $15x^2+14xy-8y^2=0$ is $\frac{3\sqrt{2}}{4}$. Reason: The product of the perpendiculars drawn from the point $(x_1,y_1)$ on the lines $a{x}^2+2hxy+b{y}^2=0$ is $\left|\frac{a{x}_1^2+2h{x}_1{y}_1+b{y}_1^2}{\sqrt{{(a-b)}^2+4h^2}}\right|$.

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• C. Assertion is correct but Reason is incorrect
• D. Both Assertion and Reason are incorrect

Answer 1

The correct option is A Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

Reason is true (from theory)
using it is assertion we have the required product
$\left|\frac{15\times 1+14\times 1\times 3-8\times 9}{\sqrt{{(1-3)}^2+{\left(14\right)}^2}}\right|=\frac{15}{10\sqrt{2}}=\frac{3\sqrt{2}}{4}$
so assertion is true.