Find The Equation Of The Tangents To The Circle x2 + y2 = 9, Which  Are Parallel To The Line 3x + 4y – 5 = 0

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Question

Find the equation of the tangents to the circle x2 + y2 = 9, which  Are parallel to the line 3x + 4y – 5 = 0

Solution

Correct option is

3x + 4y ± 15 = 0

 

Slope of   

   

and equation of circle is x2 + y2 = 9  

∴ Equation of tangents

                    

⇒              4y = –3x ± 15

or              3x + 4y ± 15 = 0

Testing

SIMILAR QUESTIONS

Q1

A circle of radius 2 lies in the first quadrant and touches both the axes of co-ordinates. Find the equation of the circle with centre at (6, 5) and touching the above circle externally.

Q2

A circle of radius 5 units touches the co-ordinates axes in first quadrant. If the circle makes one complete roll on x-axis along the positive direction of x-axis, find its equation in the new position.

Q3

 

Discuss the position of the points (1, 2) and (6, 0) with respect to the circle

                          x2 + y2 – 4x +2y – 11 = 0.

Q4

 

Find the shortest and largest distance from the point (2, –7) to the circle 

                   x2 + y2 – 14x – 10y – 151 = 0

Q5

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

Q6

Find the length of the intercept on the straight line 4x – 3y – 10 = 0 by the circle x2 + y2 – 2x + 4y – 20 = 0.

Q7

Find the co-ordinates of the middle point of the chord which the circlex2 + y2 + 4x – 2y – 3 = 0 cuts off the line x – y + 2 = 0.

Q8

For what value of λ will the line = 2x + λ be a tangent to the circle x2 +y2 = 5?

Q9

Find the equation of tangent to the circle x2 + y2 – 2ax = 0 at the point   

Q10

 

Find the equation of the tangents to the circle x2 + y2 = 9, which

Are perpendicular to the line 2x + 3y + 7 = 0.