Derive the equation of the parabola with a focus at (–5, 5) and a directrix of y = -1.

Step-by-step explanation:

We are given that focus of parabola at (-5,5).

Equation of directrix y=-1

We have to derive the equation of parabola

We know that the parabola is the set of points (x,y) equally distant from (-5,5) and (x,-1).

Distance formula

Apply this formula

Squaring on both sides then we get

 ()

This is required equation of parabola along y- axis.

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'.