Find the Cartesian equation of the circle whose parametric equations are x = 3 cos θ, y = 3 sin θ, 0 ≤ θ ≤ 2π. - Business Mathematics and Statistics

Find the Cartesian equation of the circle whose parametric equations are x = 3 cos θ, y = 3 sin θ, 0 ≤ θ ≤ 2π.

Sum

Given x = 3 cos θ, y = 3 sin θ

Now x² + y² = 9 cos²θ + 9 sin²θ

x² + y² = 9 (cos²θ + sin²θ)

x² + y² = 9 which is the Cartesian equation of the required circle.

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Chapter 3: Analytical Geometry - Exercise 3.4 [Page 64]

Chapter 3 Analytical Geometry
Exercise 3.4 | Q 9 | Page 64

Find the centre and radius of the circle.

(x + 2) (x – 5) + (y – 2) (y – 1) = 0

Find the equation of the circle whose centre is (2, 3) and which passes through (1, 4).

The length of the tangent from (4, 5) to the circle x² + y² = 16 is:

If the perimeter of the circle is 8π units and centre is (2, 2) then the equation of the circle is:

Find the equation of the circle with centre (2, −1) and passing through the point (3, 6) in standard form

Find the equation of the tangent and normal to the circle x² + y² – 6x + 6y – 8 = 0 at (2, 2)

If the equation 3x² + (3 – p)xy + qy² – 2px = 8pq represents a circle, find p and q. Also determine the centre and radius of the circle

Choose the correct alternative:

The centre of the circle inscribed in a square formed by the lines `x^2 - 8x - 12` = 0 and `y^2 - 14y + 45` = 0 is

Choose the correct alternative:

The radius of the circle passing through the points (6, 2) two of whose diameter are x + y = 6 and x + 2y = 4 is

Choose the correct alternative:

The circle passing through (1, – 2) and touching the axis of x at (3, 0) passing through the point