The correct option is D 7x−4y−15=0
Given circle is
x2+y2−10x−10y+25=0
C=(5,5),r=5
Equation of polar when pole is (1,−2) is
x−2y−5(x+1)−5(y−2)+25=0⇒−4x−7y+30=0⇒4x+7y−30=0
Distance from centre to polar is
|20+35−30|√65=25√65<5
So, polar is a chord
The diameter which bisects the chord is perpendicular to it, so
7x−4y+λ=0
It passes through centre (5,5)
⇒35−20+λ=0⇒λ=−15
Hence, the required equation of the diameter is
7x−4y−15=0