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The points of intersection of the line 4...

The points of intersection of the line `4x-3y-10=0` and the circle `x^2+y^2-2x+4y-20=0` are ________ and ________

Text Solution

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The correct Answer is:
`(-2, - 6) and (4, 2)`
For point of intersection, we put
`x=(3y+10)/(4)" in " x^(2)+y^(2)-2x+4y-20=0`
`rArr ((3y+10)/(4))^(2)+y^(2)-2((3y+10)/(4))+4y-20=0`
`rArr 25y^(2)+100y-300=0`
`rArr y^(2)+4y-12=0`
`rArr (y-2)(y+6)=0`
`rArr y = -6 ,2`
when y = -6 `rArr` x = -2
when y = 2
`rArr x = 4
`therefore` point intersection are (-2, -6) and (4, 2).
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