Shortest distance from a point to a line-
write an equation for the parabola with vertex at (3,-5) and going through (1,-8)

The equation of parabola in vertex form is

Solution:

Given that parabola with vertex (3, -5) and going through point (1, -8)

To find : equation of parabola

The equation of parabola in vertex form is given as:

 ----- eqn 1

where (h, k) are the coordinates of the vertex

here (h, k) = (3, −5)

Substituting the values in above formula, we get

 ----- eqn 2

The given equation of parabola passes through (1, -8)

Substituiting (x, y) = (1, -8) in eqn 2 we get,

Now substitute the value of "a" in eqn 2,

Thus the equation of parabola in vertex form is found

n=9

step-by-step explanation:

7 times a number = 7n

decreased by 13 = 7n-13

same as is =

5 times the number = 5n

increased by 5 = 5n+5

7n-13 = 5n+5

2n=18

n=9

center (1,3) with radius 6

step-by-step explanation:

we must complete the square to find the center and radius of the circle.

first make sure the x and y squared terms have 1 as their coefficients. we also make sure x and y terms together.

we now create space between the x and y terms with parenthesis.

we complete the square by taking the middle terms -2x and the -6y - divide each and square them.

we add the squares to both sides.

simplify.

and write the quadratics in factored form.

the center is (h,k) or (1,3). the radius is the square root of 36 which is 6.