Tangent Which Is Parallel To The Line x – 3y – 2 = 0 Of The Circle x2 + y2 – 4x + 2y – 5 = 0, Has Point/points Of Contact.  

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Question

Tangent which is parallel to the line x – 3y – 2 = 0 of the circle x2 + y2 – 4x + 2y – 5 = 0, has point/points of contact.  

Solution

Correct option is

(3, –4)

Equation of the given line is  

                   x – 3y – 2 = 0                        …(1)  

equation of the circle 

                   x2 + y2 – 4x + 2y – 5 = 0       …(2)  

equation of the tangent at (x1y1) to the circle (2) is  

                     

                     

                      

Lines (1) & (2) are || so  

                     

                   

and             y1 + 1 = –3 

                   y1 = –4  

So the point of contact (3, – 4).

Testing

SIMILAR QUESTIONS

Q1

The normal 3x – 4y = 4 and 6x – 8y – 7 = 0 are tangents to the circle. Then its radius is:

Q2

The circle x2 + y2 + x + y = 0 and x2 + y2 + x – y = 0 intersect at the angle of:

Q3

Find the radical centre of the circles, x2 + y2 + 3x + 2y + 1 = 0,  x2 + y2 – x + 6y + 5 = 0, x2 + y2 + 5x – 8y + 15 = 0

Q4

The tangents drawn from the origin to the circle x2 + y2 – 2kx – 2ry + r2 = 0 are perpendicular, if:

Q5

The locus of the mid points of a chord of the circles x2 + y2 = 4, which subtends a right angle at the origin is:

Q6

The chord of contact of tangents from a point P to a circle passes through Q, if l1 and l2 are the lengths of tangents from P and Q to the circle, then PQ is equal to:

Q7

Find the equation of the chord of x2 + y2 – 6x + 10y – 9 = 0 which is bisected at (–2, 4). 

Q8

Find the middle point of the chord intercepted on line lx + my + n = 0 by the circle x2 + y2 = a2.  

Q9

Find the power of the point (2, 4) with respect to the circle. x2 + y2 – 6x+ 4y – 8 = 0