Question

Assertion :Slope of tangents drawn from $(4,10)$ to parabola $y^2=9x$ are $\frac{1}{4},\frac{9}{4}$ Reason: Every parabola is symmetric about its directrix

• 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

Equation of tangent is $y=mx+\frac{a}{m}$
Since it passes through $(4,10)$

$\Rightarrow 10=4m-1\frac{\frac{9}{4}}{m}\Rightarrow 16m^2-40m+9=0$

If the roots of this quadratic equation are $m_1$ and $m_2$, then
$m_1+m_2=\frac{40}{16}=\frac{5}{2};m_1{m}_2=\frac{9}{16}\Rightarrow m_1=\frac{1}{4},m_2=\frac{9}{4}$
And every parabola is symmetric about its axis hence only assertion is true