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.