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Equation of the tangent to the curve 2x^...

Equation of the tangent to the curve `2x^(2)+3y^(2)-5=0` at (1, 1) is

A

`2x-3y-5=0`

B

`2x+3y-5=0`

C

`2x+3y+5=0`

D

`3x+2y+5=0`

Text Solution

Verified by Experts

The correct Answer is:
B
Equation of the curve is
`2x^(2)+3y^(2)-5=0`
Differentiating w. r.t.x, we get
`4x+6y.(dy)/(dx)=0`
`:.(dy)/(dx)=(-4x)/(6y)=(-2x)/(3y)`
`:.` Slope of the tangent `=(dy)/(dx)=(-2x)/(3y)`
At point `(1,1)((dy)/(dx))_(((1,1)))=(-2)/(3)`
`:.` Equation of tangent at (1,1),
`y-y_(1)=(dy)/(dx)(x-x_(1))`
`y-1=(-2)/(3)(x-1)`
`:.3y-3=-2x+2`
`2x+3y-5=0`
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Knowledge Check

  • The equation of tangent to the curve 2x^(2)+3y^(2)-5=0 at (1,1) is

    A
    2x+3y+5=0
    B
    2x-3y-5=0
    C
    2x-3y+5=0
    D
    2x+3y-5=0

  • Equation of the tangent to the curve x^(n)-y^(n)=0 at (2, 2) is

    A
    `ny+x-4=0`
    B
    `x=2n`
    C
    `y=2n`
    D
    `y=x`

  • The equation of the tangent to the curve x^(2)-2xy+y^(2)+2x+y-6=0 at (2,2) is

    A
    `2x+y-6=0`
    B
    `2y+x-6=0`
    C
    `x+3y-8=0`
    D
    `3x+y-8=0`

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