Question

Find the pole of 3x+4y-45=0 with respect to X2+y2-6x-8y+5=0

Answer 1

Answer:

given line equation 3x+4y-45=0 compare with lx+my+n=0.

therefore l=3,m=4,n=-45.

circle equation x^2+y^2-6x-8y+5=0 compare with x^2+y^2+2gx+2fy+c=0.

therefore 2g=-6,2f=-8,c=5

g=-3,f=-4

r=√g^2+f^2-c. =√9+16-5. =√20. pole=(6,8).

Answer 2

Concept: z0 is the pole of the function.

Given: 3x+4y-45=0

X2+y2-6x-8y+5=0

Find: Find the point of pole.

Solution:

3x+4y-45=0 →(1)

Let (x1,y1) is the pole

Equation of (x1,y1) of polar is S1=0

= x(x1-3)+y(y1-4)-3x1-4y1+5=0 →(2)

Compare equation (1) and equation (2)

x1-3=3             y1-4=4

x1=6                 y1=8

(6,8)

Final answer: The pole of 3x+4y-45=0 with respect to X2+y2-6x-8y+5=0 is (6,8).

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