Advertisement Remove all ads

The Vertex of the Parabola X2 + 8x + 12y + 4 = 0 is - Mathematics

MCQ

The vertex of the parabola x2 + 8x + 12y + 4 = 0 is

Options

  • (−4, 1) 

  • (4, −1) 

  •  (−4, −1) 

  • (4, 1) 

Advertisement Remove all ads

Solution

 (−4, 1) 

Given:
x2 + 8x + 12y + 4 = 0 

\[\Rightarrow \left( x + 4 \right)^2 - 16 + 12y + 4 = 0\]
\[ \Rightarrow \left( x + 4 \right)^2 + 12y - 12 = 0\]
\[ \Rightarrow \left( x + 4 \right)^2 = - 12\left( y - 1 \right)\]

Let \[X = x + 4, Y = y - 1\] 

∴ \[X^2 = - 12Y\] 

Vertex = \[\left( X = 0, Y = 0 \right) = \left( x + 4 = 0, y - 1 = 0 \right) = \left( x = - 4, y = 1 \right)\] 

Hence, the vertex is at (−4, 1). 

  Is there an error in this question or solution?
Advertisement Remove all ads

APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 25 Parabola
Q 16 | Page 30
Advertisement Remove all ads

Video TutorialsVIEW ALL [1]

Advertisement Remove all ads
Share
Notifications

View all notifications


      Forgot password?
View in app×