Question

The locus of the point of intersection of the tangent to the circle x = r cos θ, y = r sin θ at points whose parametric angles differ by

 is 

Solution

Correct option is

Tangent at θ = 0 and θ = π/3 are x = r and x cos (π/3 + y sin (π/3) = r   

  

SIMILAR QUESTIONS

Q1

If C1C2 are the centre of these circles than area of Δ OC1 C2, where Ois the origin, is

Q2

A triangle has two of its sides along the axes, its third side touches the circle x2 + y2 – 2ax – 2ay + a2 = 0. If he locus of the circumcentre of the triangle passes through the point (38, –37) then a2 – 2a is equal to

Q3

Two circles are inscribed and circumscribes about a square ABCD, length of each side of the square is 32. P and Q are points respectively of these circles, then  is equal to

Q4

Let A be the centre of the circle x2 + y2 – 2x – 4y – 20 = 0. The tangents at the point B(1, 7) and C(4, –2) on the circle meet at the point D. If Δ denotes the area of the quadrilateral ABCD, then 45Δ is equal to

Q5

If four distinct points (2, 3), (0, 2), (4, 5) and (0, t) are concylic, then t3+ 17 is equal to 

Q6

Equation of a tangent to the circle with centre (2, –1) is 3x + y = 0. The squar  of the length of the tangent to the circle from the point (23, 17) is

Q7

The centres of two circles C1 and C2 each of unit radius are at a distance of 6 units from each other. Let P be the mid-point of the line segment joining the centres of C1 and C2 and C be a circle touching C1 and C2externally. If a common tangent to C1 and C passing through P is also a common tangent to 2 and C1, then the radius of the circle C is 

Q8

An equation of the circle through (1, 1) and the points of intersection ofx2 + y2 + 13x – 3y = 0 and 2x2 + 2y2 + 4x – 7y – 25 = 0 is   

Q9

The abscissae of two points A and B are the roots of the equation x2 + 2ax – b2 = 0, and their ordinates are the roots of the equation x2 + 2px –q2 = 0. The radius of the circle with AB as diameter is  

Q10

The locus of a point which moves such that the tangents from it to the two circles x+ y2 – 5x – 3 = 0 and 3x2 + 3y2 + 2x + 4y – 6 = 0 are equal is