Question

(e) If the line 2x+6y=5 intersect the
X-axis, then find its coordinate.
(1) (-2-5,0) (ii) (2.5,0)
(iii) (0,2-5) (iv) (0, -2.5)​

Answer 1

Answer:

Correct answer is x2+y2

−10x−10y+25=0

Let the required equation be x

2

+y

2

+2gx+2fy+c=0

It passes through the point (2,1)

⟹4+1+4g+2f+c=0

4g+2f+c+5=0⋯(1)

It touches x-axis

⟹g

2

−c=0

g

2

=c⋯(2)

It touches y-axis

⟹f

2

−c=0

f

2

=c⋯(3)

From (2),(3)

g

2

=f

2

⟹g=f⋯(4)

Put (2)(4) in (1)

⟹4g+2g+g

2

+5=0

g

2

+6g+5=0

(g+1)(g+5)=0

g=−1,−5

Put g=−5⟹f=−5⟹c=25

So the required Equation is x

2

+y

2

−10x−10y+25=0