A tangent having slope of -4 / 3 to the ellipse ( x 2/18)+( y 2/32)=1 intersects the major and minor axes at points A and B, respectively. If C is the center of the ellipse, then the area of triangle ABC is

Question

A tangent having slope of -4 / 3 to the ellipse ( x 2/18)+( y 2/32)=1 intersects the major and minor axes at points A and B, respectively. If C is the center of the ellipse, then the area of triangle ABC is (A) 12 sq. units (B) 24 sq. units (C) 36 sq. units (D) 48 sq. units

Tardigrade Admin · Accepted Answer

One of the tangents of slope m to the given ellipse is y=m x+√18 m2+32 For m =-4 / 3, we have y=-4 / 3 x+8 Then points on the axis where the tangents meet are A (6,0) and B (0,8) Then the area of triangle ABC is (1/2)(6)(8)=24 units

Q. A tangent having slope of $- 4/3$ to the ellipse $\frac{x ^{2}}{18} + \frac{y ^{2}}{32} = 1$ intersects the major and minor axes at points $A$ and $B$ , respectively. If $C$ is the center of the ellipse, then the area of triangle $A BC$ is

12 sq. units

24 sq. units

36 sq. units

48 sq. units

One of the tangents of slope $m$ to the given ellipse is
$y = m x + 18 m^{2} + 32$
For $m = - 4/3$ , we have
$y = - 4/3 x + 8$
Then points on the axis where the tangents meet are $A (6, 0)$ and $B (0, 8)$
Then the area of triangle $A BC$ is
$\frac{1}{2} (6) (8) = 24$ units

Q. A tangent having slope of −4/3 to the ellipse 18x2​+32y2​=1 intersects the major and minor axes at points A and B, respectively. If C is the center of the ellipse, then the area of triangle ABC is