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Find the equation of the tangent to the ...

Find the equation of the tangent to the parabola `9x^2+12 x+18 y-14=0` which passes through the point (0, 1).

Text Solution

Verified by Experts

The correct Answer is:
`4x+3y-3=0andy-1=0`
The line passing through the point (0,1) having slope m is
`y-1=m(x-0)ory=mx+1`.
Solving this line with given parabola, `9x^(2)+12x+18y-14=0`
we have
`9x+12x+18(mx+1)-14=0`
`or" "9x^(2)+6(2+3m)x+4=0`
Since the touches the parabola, the above equation equation will have equal roots, i.e.,
D=0
`or" "36(2+3m)^(2)-4(36)=0`
`or" "9x^(2)+12m=0`
`i.e.," "m=0orm=(-4)/(3)`
So, the equation of tangents are 4x+3y-3=0 and y-1=0.
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