Search any question & find its solution
Question:
Answered & Verified by Expert
If $(2,0)$ is the vertex and the $y$ -axis is the directrix of a parabola, then where is its focus?
Options:
Solution:
1331 Upvotes
Verified Answer
The correct answer is:
$(4,0)$
Vertec is $(2,0)$. Since, $y$ -axis is the directrix of a parabola. Equation directrix is $x=0 .$ So, axis of parabolais $x$ -axis. Let the focus be $(\mathrm{a}, 0)$
Distance of the vertex of a parabola from directrix = its distance from focus
So, $\mathrm{OV}=\mathrm{VF} \Rightarrow(2-0)^{2}=(\mathrm{a}-2)^{2}$
$a^{2}=4 a b a=4$
$\Rightarrow$ Focus is $(4,0)$
Distance of the vertex of a parabola from directrix = its distance from focus
So, $\mathrm{OV}=\mathrm{VF} \Rightarrow(2-0)^{2}=(\mathrm{a}-2)^{2}$
$a^{2}=4 a b a=4$
$\Rightarrow$ Focus is $(4,0)$
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.