Question

Assertion :The line $bx-ay=0$ will not meet the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ $(a>b>0)$ Reason: The line $y=mx+c$ does not meet the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ if $c^2=a^2{m}^2-b^2$

• 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 C Assertion is correct but Reason is incorrect

If we solve $bx-ay=0$ and $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$
We get, $0=1\Rightarrow$ no solution showing that statement-l is true.
But the statement-2 is false as the line $y=mx+c$ is a tangent to the hyperbola if $c^2=a^2{m}^2-b^2$ so the line meets the curve at one point.