Question

if 4x-3y+7=0is a tangent to the circle represented by x²+y²-6x+4y-12=0 then find its point of contact.
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Answer 1

Answer:

It is given that 4x−3y+7=0 is a tangent to the circle x  

2

+y  

2

−6x+4y−12=0. The centre of the circle C is (3,−2). The line will touch the circle at the foot of the perpendicular from the centre (property of tangent).

Foot of the perpendicular from C to tangent

4

h−3

​  

=  

−3

k+2

​  

=−  

4  

2

+3  

2

 

​  

 

4(3)−3(−2)+7

​  

 

⇒  

4

h−3

​  

=−  

25

25

​  

 and −  

3

k+2

​  

=−  

25

25

​  

 

⇒h−3=−4 and k+2=3

⇒h=−1 and k=1

Hence the point of contact is (−1,1)

Step-by-step explanation:

Answer 2

Answer:

It's easy...

There is already an answer written by using simple coordinate geometry, so I would like to solve it by... DIFFERENTIAL CALCULUS.

Hope this helps.

Step-by-step explanation:

Check the attachment for your answer