Question

The parabola $x^2=py$ passes through $(12,16).$
Then the focal distance of the point is

• A. $\frac{57}{4}$
• B. $\frac{73}{4}$
• C. $13$
• D. $18$

Answer 1

The correct option is B

$\frac{73}{4}$

Given,
Parabola : $x^2=py$

As $x^2=py\text{passes through}(12,16)$
$\Rightarrow {\left(12\right)}^2=p\times 16$
$\Rightarrow 144=p\times 16\Rightarrow p=9$
Hence, we get
$x^2=9y$
Compare it with $x^2=4ay$
$4a=9\Rightarrow a=\frac{9}{4}$
$\text{focal distance}=|y_1+a|\text{here}{y}_1=16\Rightarrow \text{focal distance}=|16+\frac{9}{4}|\Rightarrow \text{focal distance}=\frac{73}{4}$
Hence, the correct answer is Option b.