wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

The equation of the parabola whose focus is at (−1,−2) and the directrix is the line x−2y+3=0

A
4x2+y2+4xy+4x+32y+16=0
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
4x2+y2+4xy+2x+8y+16=0
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
4x2+y2+4xy+40x+16y+16=0
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
4x2+4y2+4xy+4x+32y+16=0
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is A 4x2+y2+4xy+4x+32y+16=0
Let P(x,y) be any point on the parabola whose focus is S(1,2) and the directrix x2y+3=0.

Now, distance of P from focus = distance of P from directrix.
(x+1)2+(y+2)2=|x2y+3|1+4
(x+1)2+(y+2)2=(x2y+31+4)2
5[(x+1)2+(y+2)2]=(x2y+3)25(x2+y2+1+2x+4y+4)=(x2+4y2+94xy+6x12y)4x2+y2+4xy+4x+32y+16=0

This is the equation of the required parabola.

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Parabola
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon