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BITSAT 2009
Exam
BITSAT
Year
2009
Subject
Mathematics
Chapter
Functions

BITSAT 2009 · Mathematics · Functions

Find the vertex of the parabola x²-8 y-x+19=0 .

Find the vertex of the parabola x2−8y−x+19=0x²-8 y-x+19=0.

Options

  1. A((12,7532)\left(\frac{1}{2}, \frac{75}{32}\right))
  2. B((15,6532)\left(\frac{1}{5}, \frac{65}{32}\right))
  3. C((13,6522)\left(\frac{1}{3}, \frac{65}{22}\right))
  4. D((13,3512)\left(\frac{1}{3}, \frac{35}{12}\right))

Correct answer

A. ((12,7532)\left(\frac{1}{2}, \frac{75}{32}\right))

Step-by-step solution

The given equation of Parabola can be written as \lleft(x−12)2−8y+19−14=0 and  \lleft(x−12)2=8y−76−14 and ⇒\lleft(x−12\rright)2=8\lleft(y−7532)∴ vertex =(12,7532)\begin{aligned} \lleft(x-\frac{1}{2})^2-8 y+19-\frac{1}{4}=0 \\ \text{\text{ and } } \lleft(x-\frac{1}{2})^2=8 y-\frac{76-1}{4}\\ \text{ and } \Rightarrow\lleft(x-\frac{1}{2}\rright)^2=8\lleft(y-\frac{75}{32}) \therefore \text{ vertex }=\left(\frac{1}{2}, \frac{75}{32}\right) \end{aligned})$
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