Find the equations of the circles satisfying the given conditions : 1)touches y axis at (0, 3) and passes through - Maths - Conic Sections

Question

Find the equations of the circles satisfying the given conditions
:
1)touches y axis at (0,?3) and passes through (-1,0)
2)touches the line 2x-3y-7=0 at (2,-1) and passes through (4,1)
3)touches the line 3x+y+3=0 at (-3,6) and tangent x+3y-7=0

Neha Sethi · Accepted Answer

Dear student
Assuming in part 1) the point as 0,3Let (h,k) be centre of circle
Circle touches the y-axisSo, radius will be h
Equation of circlex-h2+(y-k)2=h2It touches the y-axis at 0,30-h2+(3-k)2=h2⇒h2+(3-k)2=h2⇒(3-k)2=0⇒3-k=0⇒k=3It passes through the point -1,0So,-1-h2+(0-3)2=h2⇒1+h2+2h+3=h2⇒4+2h=0⇒h=-2So, equation of circle is x+22+(y-3)2=(-2)2⇒x+22+(y-3)2=4
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Find the equations of the circles satisfying the given conditions : 1)touches y axis at (0,?3) and passes through (-1,0) 2)touches the line 2x-3y-7=0 at (2,-1) and passes through (4,1) 3)touches the line 3x+y+3=0 at (-3,6) and tangent x+3y-7=0.

Find the equations of the circles satisfying the given conditions :
1)touches y axis at (0,?3) and passes through (-1,0)
2)touches the line 2x-3y-7=0 at (2,-1) and passes through (4,1)
3)touches the line 3x+y+3=0 at (-3,6) and tangent x+3y-7=0.