Question

Assertion :If the line $y=3x+\lambda$ touches the hyperbola $9x^2-5y^2=45$ then $\lambda =\pm 6$. Reason: $c^2=a^2{m}^2-b^2$ is the condition for the line $y=mx+c$ touches the hyperbola.

• 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

Given $y=3x+\lambda ....\left(i\right)$ &
$9x^2-5y^2=45....\left(ii\right)$ $\Rightarrow \frac{x^2}{5}-\frac{y^2}{9}=1$ $\Rightarrow a^2=5,b^2=9,$
Now line (i) will touch the hyperbola
If, $c^2=a^2{m}^2-b^2$
$\Rightarrow {\lambda }^2=5(3{)}^2-9=36$ $\therefore \lambda =\pm 6$