Q1. Show that for all values of p, the circle x2 + y2 - x(3p+4) –y(p-2) + 10p =0 passes through the point (3,1). If p varies, find the locus of the centre of the above circle.
Q2. Whatever be the values of θ, prove that the locus of the point of intersection of the straight lines y =atanθ and asin3θ + ycos3θ = asinθcosθ is a circle. Find the equation of the circle.
Q3. Prove that the square of the distance between the two points (x1 , y1) and (x2 , y2) of the circle x2 +y2 = a2 is 2(a2-x1x2-y1y2).
Q1. Show that for all values of p, the circle x2 + y2 - x(3p+4) –y(p-2) + 10p =0 passes through the point (3,1). If p varies, find the locus of the centre of the above circle.
Q2. Whatever be the values of θ, prove that the locus of the point of intersection of the straight lines y =atanθ and asin3θ + ycos3θ = asinθcosθ is a circle. Find the equation of the circle.
Q3. Prove that the square of the distance between the two points (x1 , y1) and (x2 , y2) of the circle x2 +y2 = a2 is 2(a2-x1x2-y1y2).
Arindam Dutta , 13 Years ago
Grade 12
