Question

Please help me Asap!​

Answer 1

Answer:

Slope of tangent to the curve 4x

2

+9y

2

=36 is 1. since it is equally inclined to the axes.

dx

dy

=

9y

4x

=1

⇒x=

4

9y

On solving obtained equation with the equation of curve, we get y=±

13

4

Substituting value of y we get (x,y)=(

13

9

,

13

4

),(−

13

9

,

13

4

),(

13

9

,−

13

4

)

Hence, options 'A', 'B' and 'C' are correct.

Answer 2

How to determine the equation of a tangent:

Determine the equation of the circle and write it in the form \[(x - a)^{2} + (y - b)^{2} = r^{2}\]

From the equation, determine the coordinates of the centre of the circle \((a;b)\).

Determine the gradient of the radius: \[m_{CD} = \frac{y_{2} - y_{1}}{x_{2}- x_{1}}\]