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

The vertices of the base of an isosceles triangle lie on the parabola x2=4y and the base is a part of the line x=2y−4. If the third vertex of the triangle lies on y-axis, then

A
one of the vertices of the triangle is (0,92)
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
one of the vertices of the triangle is (4,4)
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C
Area of the triangle is 15 sq. units
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
Centroid of the triangle is (23,196)
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
Open in App
Solution

The correct options are
A one of the vertices of the triangle is (0,92)
B one of the vertices of the triangle is (4,4)
D Centroid of the triangle is (23,196)
x2=4y and x=2(y2)
4(y2)2=4y
y=1,4
x=2(y2)x=2,4
B(2,1), C(4,4)

Now, AB=AC
(0+2)2+(y1)2=(04)2+(y4)2
4+y22y+1=16+y28y+16
y=92
A(0,92)

Area of triangle
=12∣ ∣ ∣ ∣0921211441∣ ∣ ∣ ∣=7.5 sq. units

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