CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon


Question

A tangent having slope of 43 to the ellipse x218+y232=1 intersects the major and minor axes at point A and B respectively. If C is the centre of the ellipse, then the area of the triangle ABC (in sq. unit) is 


Solution

One of the tangent with slope m to the ellipse x218+y232=1 is:
y=mx+18m2+32
Given, m=43
y=43x+8
This line intersect coordinate axis at A(0,8),B(6,0) and C is (0,0)
Then, area of triangle ABC
=12(6)(8)=24 sq. units


Alternate Solution:
Equation of tangents with slope m=43 to the ellipse x218+y232=1 is :
y=mx±18m2+32
y=43x±8
This line intersect coordinate axis at A(0,±8),B(±6,0) and C is (0,0).
If we consider first quadrant, then coordinates are A(0,8),B(6,0) and C(0,0).
Then, area of triangle ABC
=12(6)(8)=24 sq. unit.
If we consider third quadrant, then coordinates are A(0,8),B(6,0) and C(0,0).
Then, area of triangle ABC
=12(6)(8)=24 sq. unit.

flag
 Suggest corrections
thumbs-up
 
0 Upvotes


Similar questions
View More


People also searched for
View More



footer-image