Find an equation of the tangent to the curve at the given point by both eliminating the parameter and without eliminating the parameter. x = 6 + ln(t), y = t2 + 6, (6, 7)

2x-y=5

Step-by-step explanation:

Given

without eliminating parameter

=

=2t

at

6=6+

t=1

Equation of line is given by

2=

2x-12=y-7

2x-y=5

by eliminating parameter

differentiating we get

2x-y=5

b. an equilateral triangle inscribed in a circle

step-by-step explanation:

we are given the figure of two circles having a triangle inside.

now, we know that,

"when a figure is lying inside an another figure, then the outside figure is known as circumscribed figure and the figure lying inside is referred to as the inscribed figure".

as we see that, the circles are containing the triangle completely.

thus, the circles are the circumscribed figures and the triangle is the inscribed figure.

hence, we get, 'an equilateral triangle is inscribed in a circle'.