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Grade 12Analytical Geometry

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

14 Years agoGrade 12

1 Answer

Shyama P

Approved Tutor Answer14 Years ago

Q1:

put x=3, y=1 in the eq. U get 9+1-3(3p+4)-(p-2)+10p=12-12-10p+10p=0.

ie. For any value of p the pt.(3,1) satisfy the eq. Hence proved.

Let center be (h,k). From eq.

h=(3p+4)/2 => p=(2h-4)/3

k=(p-2)/2 . Sub. value of p we get:

3k-h+5=0

ie. locus of center is:

3y-x+5=0 ie. straight line

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