Find an equation of the tangent to the curve at the given point by both eliminating the parameter and without eliminating the parameter. x = 5 + ln(t), y = t2 + 2, (5, 3)

Step-by-step explanation:

Given that:

At point (5,3)

To find an equation of the tangent to the curve at the given point,

By without eliminating the parameter

t²  + 5 = 4

t² = 4 - 5

t² = - 1

Then;

The equation of the tangent  is:

y - 3 = -2x +10

y = -2x + 7

y = 2x - 7

By eliminating the parameter

x = 5 + In(t)

In(t)  = 5 - x

The equation of the tangent  is:

y - 3 = -2x +10

y = -2x + 7

y = 2x - 7

answer: a and c are correct

step-by-step explanation:

the +5 is the vertical translation

the added negative symbol in front is the reflection over the y-axis