# 25) Find the equation of the tangent to the curve  which is parallel to the line

Parellel to line  means the slope of tangent and slope of line is equal
We know that the equation of line is
y = mx + c
on comparing with the given equation we get the slope of line m = 2 and c = 5/2
Now, we know that the  slope of the tangent at a given point to given curve is given by
Given the equation of curve is

Now, when

,

but y cannot be -ve so we take only positive value
Hence, the coordinates are

Now, equation of tangent paasing through

and with slope m = 2 is

Hence, equation of tangent paasing through  and with slope m = 2 is   48x - 24y = 23

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