Question

Generic question 16

Answer the question

Answer 1

Equation of Circle :
${(x + 9)}^{2} + {(y - 1)}^{2} = 50$

Theorem Used :
1) Perpendicular from the centre bisect the
chord .

All measurements are given in general units .
Steps involved :

We will first try to find its radius and then centre to get equation of circle .

For Calulation see Pics

1) OP = CT = 4√2
Distance between parallel lines.

2) TR = 6√2/2=3√2
By Theorem 1 .


Now, By pythagoras theorem in CTR ,
CR = 5√2


3)Since , Point P lies on line y = x :

Let P be (h,h) .
By distance formula in.OP.

Then , h = -4 as Circle lies in left side of y - axis i.e - x axis .


4) Using , tan (45°) in triangle CBA and APO.

CB = AB = a (say)
Then , CA = a√2.( By PT)

5) CP = CA + AP

=> CA = √2
=> a = 1.

6) AO = 8 .
AB = 1

Looking at the figure ,
Centre : (-9,1)
Radius = 5√2 .


Hence, required equation of circle
${(x + 9)}^{2} + {(y - 1)}^{2} = 50$



Hope, you understand my answer .