Question

 

If the parametric of form of a circle is given by

(i) x = – 4 + 5 cos θ and y = – 3 + 5 sin θ  

(ii) x = a cos α + b sin α and y = a sin α – b cos α

Find its Cartesian form.

Solution

Correct option is

 

(i) The given equations are

             x = – 4 + 5 cos θ and y = – 3 + 5 sin θ

or             (x + 4) = 5 cos θ         …(1)

an d          (y + 3) = 5 sin θ         …(2)

Squaring and adding (1) and (2), then

             (x + 4)2 + (y + 3)2 = 52

or         (x + 4)2 + (y + 3)2 = 25 

(ii) The given equations are

             x = a cos α + b sin α             …(1)

             y = a sin α + b cos α             …(2)

Squaring and adding (1) and (2), then

            

SIMILAR QUESTIONS

Q1

Suppose ax + bx + c = 0, where abc are in A.P. be normal to a family or circles. The equation of the circle of the family which intersects the circle x2 + y2 – 4x – 4y – 1 = 0 orthogonally is

Q2

Find the equation of chord of x2 + y2 – 6x + 10y – 9 = 0 which is bisected at (–2, 4).

Q3

Find the equation of that chord of the x2 + y2 = 15 which is bisected at (3, 2).

Q4

 

Find the centre and radius of the circle 

             2x2 + 2y2 = 3x – 5y + 7

Q5

Find the equation of the circle whose centre is the point of intersection of the lines 2x – 3y + 4 = 0 and 3x + 4y – 5 = 0 and passes through the origin.

Q6

Find the equation of the circle concentric with the circle x2 + y2 – 8x + 6y– 5 = 0 and passing through the point (–2, –7).

Q7

A circle has radius 3 units and its centre lies on the line y = x – 1. Find the equation of the circle if it passes through (7, 3).

Q8

 

Find the area of an equilateral triangle inscribed in the circle

                       x2 + y2 + 2gx + 2fy + c = 0     

Q9

 

Find the parametric form of the equation of the circle

                               x2 + y2 + px + py = 0

Q10

Find the equation if the circle the end points of whose diameter are the centres of the circle x2 + y2 + 6x – 14y = 1 and x2 + y2 – 4x + 10y = 2.