Q55 / 125 · BITSAT 2009 · Mathematics
Find the vertex of the parabola \(x^2-8 y-x+19=0\).
- Correct answerA\(\left(\frac{1}{2}, \frac{75}{32}\right)\)
- B\(\left(\frac{1}{5}, \frac{65}{32}\right)\)
- C\(\left(\frac{1}{3}, \frac{65}{22}\right)\)
- D\(\left(\frac{1}{3}, \frac{35}{12}\right)\)
Solution
The given equation of Parabola can be written as
\(\begin{aligned}
&\left(x-\frac{1}{2}\right)^2-8 y+19-\frac{1}{4}=0 \\
&\left(x-\frac{1}{2}\right)^2=8 y-\frac{76-1}{4} \\
& \Rightarrow\left(x-\frac{1}{2}\right)^2=8\left(y-\frac{75}{32}\right) \therefore \text { vertex }=\left(\frac{1}{2}, \frac{75}{32}\right)
\end{aligned}\)
Hence, the correct answer is option: 'A'.