Question

Ques. 42 (MMCQ)
varks. +41
Consider the circle x2 + y2 - 8x - 18y + 93 = 0 with centre 'C' and point P(2,5) outside it. From the point P, a
pair of tangents PQ and PR are drawn to the circle with S as the midpoint of QR. The line joining P to C
intersects the given circle at A and B. Which of the following hold(s) good?
А
CP is the arithmetic mean of AP and BP
B
PR is the geometric mean of PS and PC
С
PS is the harmonic mean of PA and PB
D
The angle between the two tangents from P is tan-(4/3)​

Answer 1

Answer:

Step-by-step explanation:

joint equation of tangents

ss1=t^2

s=x^2+y^2-8x-18y+93=0

s1=16

t=-2x-4y+40

(x^2+y^2-8x-18y+93)(16) =( 2x+4y-40)^2

x^2+y^2-8x-18y+93*4 = x^2+4y^2+400+4xy-80y-40x

4x^2+4y^2-32x-72y+372 = x^2+4y^2+400+4xy-80y-40x

3x^2+8x+8y-4xy-28=0

3x^2+x(8-4y)+8y-28=0

x=4y-8 plus minus root 64+16y^2-64y-96y+336 * 1/2

x=4y-8 plus minus root  16y^2+400-170y * 1/2

you will get two equations that are your drawn tangents

you can check options now