MHT CET · Maths · Parabola
The focal distance of a point on the parabola \(y^{2}=16 x\) whose ordinate is twice the abscissa, is
- A 6
- B 8
- C 10
- D 12
Answer & Solution
Correct Answer
(B) 8
Step-by-step Solution
Detailed explanation
Given curve is \(y^{2}=16 x\). Let the point be \((h, k)\). But \(2 h=k\), then \(k^{2}=16 h\)
\(
\begin{aligned}
\Rightarrow & & 4 h^{2} &=16 h \\
\Rightarrow & & h &=0, h=4 \\
\Rightarrow & & k &=0, k=8
\end{aligned}
\)
\(\therefore\) Points are \((0,0),(4,8)\).
Hence, focal distance are respectively
\(
0+4=4,4+4=8
\)
\((\because\) focal distance \(=h-a)\)
\(
\begin{aligned}
\Rightarrow & & 4 h^{2} &=16 h \\
\Rightarrow & & h &=0, h=4 \\
\Rightarrow & & k &=0, k=8
\end{aligned}
\)
\(\therefore\) Points are \((0,0),(4,8)\).
Hence, focal distance are respectively
\(
0+4=4,4+4=8
\)
\((\because\) focal distance \(=h-a)\)
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