Question

Find the equation of the normal to the circle x2 + y2 – 5x + 2y – 48 = 0 at point (5, 6).

Solution

Correct option is

14x – 5y – 10 = 0

 

Equation of the normal at (5, 6) is

              

                

             

           14x – 70 = 5y – 30

           14x – 5y – 10 = 0.

SIMILAR QUESTIONS

Q1

 

Find the equation of circle passing through the point of intersection of the circle x2 + y2 – 6x + 2y + 4 = 0 and x2 + y2 + 2x – 4y – 6 = 0 and whose centre lies on the line y = x.

Q2

Find the equation of the circle passing through the points of intersection of the circles x2 + y2 – 2x – 4y – 4 = 0 and x2 + y2 – 10x – 12y – 40 = 0.

Q3

Find the equation of circle through points of intersection of circle x2 + y2– 2x – 4y + 4 = 0 and the line x + 2y = 4 which touches the line x + 2y = 0.

Q4

Find the angle between the circles. S = x2 + y2 – 4x + 6y + 11 = 0 and 

Q5

 

Find the equation of the system of circles coaxial with the circles.

              x2 + y2 + 4x + 2y + 1 = 0, x2 + y2 – 2x + 6y – 6 = 0

Also find the equation of that particular circle whose centre lies on radical axis.

Q6

Find the locus of pole of the line lx + my + n = 0 with respect to the circle which touches y-axis at the origin.

Q7

 

Find the circle whose diameter is the common chord of the circles

x2 + y2 + 2x + 3y + 1 = 0 and x2 + y2 + 4x + 3y + 2 = 0 

S ≡ x2 + y2 + 2x + 3y + 1 = 0 S’ ≡ x2 + y2 + 4x + 3y + 2 = 0

Q8

Find the equation of circle which cuts the circle x2 + y2 + 5x + 7y + 4 = 0 orthogonally, has its centre on the line x = 2, and passes through the point (4, –1).

Q9

Find the point of intersection of the line 2x + 3y = 18 and the circle x2 +y2 = 25.

Q10

Find the equation of the tangent to the circle x2 + y2 = 16 drawn from the point (1, 4).