Question

find the equation to the tangent to the hyperbola x2/16-y2/9=1 which are parallel to the line y2=3x-4​

Answer 1

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Next similar questionQ)

Find the equation of the tangent to the curve \( x^2+3y=3\), which is parallel to the line y−4x+5=0

A)

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Equation of the tangent at (x1,y1) where slope is m is given by y−y1=m(x−x1)

Step 1:

Given curve is x2+3y=3

Let y=−x2+33

On differentiating with respect to x

∴dydx=13[−2x]

=−23x

Step 2:

Since the tangent is parallel to the line y−4x+5=0

Then slopes should be equal

Slope of the given line is 4

−2x3=4

x=−4×32

=−122

=−6

Step 3:

∴y=−(−6)2+33

=−36+33

=−333

=−11

Hence the points of contact are (−6,−11)

Step 4:

Equation of the tangent at (x1,y1) where slope is m is given by y−y1=m(x−x1)

(i.e)[y−(−11)]=4(x−(−6))

y+11=4x+6

⇒4x−y=11−6

⇒4x−y=5

Hence 4x−y=5 is the required equation.