Question

# A tangent having slope of $$-\, \displaystyle \frac{4}{3}$$ to the ellipse $$\displaystyle {\frac{x^2}{18}\, +\, \frac{y^2}{32}\, =\, 1}$$ intersects the major & minor axes in points $$A$$ & $$B$$ respectively. If $$C$$ is the centre of the ellipse then the area of the $$\triangle ABC$$ is

A
12 sq. units
B
24 sq. units
C
36 sq. units
D
48 sq. units

Solution

## The correct option is B $$24$$ sq. unitsSince the major axis is along the y-axis.$$\therefore$$ Equation of tangent is $$x\, =\, my\, +\, \sqrt {b^2m^2\, +\, a^2}$$Slope of tangent $$=\displaystyle {\frac{1}{m}\, =\, \frac{-4}{3}\, \Rightarrow\, m\, =\, \frac{-3}{4}}$$Hence, equation of tangent is $$4x + 3y = 24$$ or $$\displaystyle {\frac{x}{6}\, +\, \frac{y}{8}\, =\, 1}$$Its intercepts on the axes are $$6$$ and $$8$$.Area $$(\Delta AOB)\, =\, \displaystyle \frac{1}{2}\, \times\, 6\, \times\, 8\, =\, 24$$ sq. unitMathematics

Suggest Corrections

0

Similar questions
View More

People also searched for
View More