Question

1.The locus of the point from which the tangent to the circles x² + y² – 4 = 0 and x² + y² – 8x + 15 = 0 are equal is given by the equation.. *​

Answer 1

Step-by-step explanation:

Let the point P(x

1

,y

1

) from which length of tangent to both the circles are equal

Length of tangent =

S

11

L

1

=

x

1

2

+y

1

2

−4

L

2

=

2(x

1

2

+y

1

2

)−10x

1

+3y

1

−2

Given, L

1

=L

2

x

1

2

+y

1

2

−4

=

2(x

1

2

+y

1

2

)−10x

1

+3y

1

−2

x

1

2

+y

1

2

−4=2(x

1

2

+y

1

2

)−10x

1

+3y

1

−2

0=x

1

2

+y

1

2

−10x

1

+3y

1

+2

This is a equation of circle with centre (5,

2

−3

) and radius =

2

101

units