# How do I write an equation in general form of an ellipse with foci at (5,2) and (5, -10) and another point at (7,15)?

The equation is

The ellipse's center is

This ellipse has a major axis that is vertical.

The ellipse's equation is

Also

And

The formula is

graph{[-46.22, 46.24, -23.13, 23.13]} = (y+4)^2/365.45+(x-5)^2/329.45-1=0

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The general form of an ellipse with foci at (5,2) and (5, -10) and passing through the point (7,15) is:

((x - h)^2) / a^2 + ((y - k)^2) / b^2 = 1

Where: Center (h, k) = (5, -4) a = distance from the center to one of the vertices = 6 b = distance from the center to one of the co-vertices = 7

Therefore, the equation in general form is:

((x - 5)^2) / 36 + ((y + 4)^2) / 49 = 1

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- Two circles have the following equations #(x -1 )^2+(y -4 )^2= 36 # and #(x +5 )^2+(y +5 )^2= 81 #. Does one circle contain the other? If not, what is the greatest possible distance between a point on one circle and another point on the other?
- A triangle has vertices A, B, and C. Vertex A has an angle of #pi/2 #, vertex B has an angle of #( pi)/4 #, and the triangle's area is #45 #. What is the area of the triangle's incircle?
- A triangle has vertices A, B, and C. Vertex A has an angle of #pi/2 #, vertex B has an angle of #( pi)/4 #, and the triangle's area is #2 #. What is the area of the triangle's incircle?
- A triangle has corners at #(9 ,5 )#, #(2 ,3 )#, and #(7 ,4 )#. What is the area of the triangle's circumscribed circle?
- A circle has a center that falls on the line #y = 2/9x +8 # and passes through # ( 3 ,1 )# and #(5 ,7 )#. What is the equation of the circle?

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