MHT CET · Maths · Parabola
The length of latus -rectum of the parabola \(x^{2}+2 y=8 x-7\) is
- A 8
- B 2
- C 6
- D 4
Answer & Solution
Correct Answer
(B) 2
Step-by-step Solution
Detailed explanation
We have,
\(\begin{array}{l}
x^{2}+2 y=8 x-7 \\
x^{2}-8 x=-2 y-7 \\
x^{2}-8 x+16=-2 y-7+16 \\
(x-4)^{2}=-2 y+9 \\
(x-4)^{2}=-2(y-9 / 2)
\end{array}\)
\(\therefore\) Length of latus rectum \(=2\)
\(\begin{array}{l}
x^{2}+2 y=8 x-7 \\
x^{2}-8 x=-2 y-7 \\
x^{2}-8 x+16=-2 y-7+16 \\
(x-4)^{2}=-2 y+9 \\
(x-4)^{2}=-2(y-9 / 2)
\end{array}\)
\(\therefore\) Length of latus rectum \(=2\)
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