Question

Statement-I lf the line $x-3y+k=0$ touches the parabola $3y^2=4x$ then $k=5$

Statement - II: Equation of the tangent to $y^2=8x$ inclined at an angle ${30}^0$ to the axis is $x-\sqrt{3}y+6=0$

• A. Statement-I and Statement-II are correct
• B. Statement-I and Statement-II are not correct
• C. Statement-I is true and Statement-II is false
• D. Statement-I is false and Statement-II is true

Answer 1

Answer: (D)

Statement-I is false and Statement-II is true

For the line $lx+my+n=0$ to touch $y^2=4ax$, the condition is $ln=a{m}^2$

So in Statement I we have $l=1,m=-3,n=k$

comparing the given parabola to the standard for we get $a=\frac{1}{3}$

Putting these values in the condition we get, $k=3$

so Statement I is False.

Statement II

Tangent is inclined to axis at angle $30$ so slope $=\frac{1}{\sqrt{3}}$

The given tangent is $x-\sqrt{3}y=-6$

Thus $y=\frac{x+6}{\sqrt{3}}$

From this we see that slope of tangent is $\frac{1}{\sqrt{3}}$

So statement II is true.