What conic section is this?

Question

25x^2 + 100x + 9y^2 – 18y = 116
What conic section is this?
Thank you!

How do I write this is in the standard form of the ellipse?

Answer 1

Complete the squares in x and y to change this equation to standard form.

25x^2 + 100x + 9y^2 - 18y = 116
25(x^2 + 4x ) + 9(y^2 - 2y ) = 116
25(x^2 + 4x + 4) + 9(y^2 - 2y + 1) = 116 + 100 + 9
25(x + 2)^2 + 9(y - 1)^2 = 225

(x + 2)^2 .... (y - 1)^2
------------- + --------------- = 1
.... 9 ............. 25

This conic section is an ellipse with center (-2, 1).

A faster method:
Since the coefficients of the second degree tems are the same sign and different, the conic section is an ellipse.

Answer 2

In mathematics, a conic section (or just conic) is a curve obtained by intersecting a cone (more precisely, a circular conical surface) with a plane. A conic section is therefore a restriction of a quadric surface to the plane. The Basic Equation of a Circle What is a circle? A circle is a collection of points in a plane which are all the same distance (called the radius) from a fixed point, the centre. The equation of a circle centred on the origin and of radius r Let us first consider a circle with centre O at the origin (0, 0) with radius r. P (x, y) is a point on the circle if and only if: OP = r where r > 0. Using the distance formula we get: This should be well known to you. You should also recognise the form:

Answer 3

25x^2 +100x +9y^2 -18y = 116
25(x^2+4x) +9(y^2-2y) = 116
25(x^2+ 4x+4) +9 (y^2-2y+1) =116 +25*4+9
25(x+2)^2 +9(y-1)^2 = 225
(x+2)^2/9 +(y-1)^2/25 = 1
This is an ellipse.

Answer 4

You can rewrite it in standard form
25(x^2+4x+4)+9(y^2-2y+1)=116+100+9=225
[(x+2)^2]/9 +[(y-1)^2]/25=1
It is an ellipse.

Answer 5

its definitely an ellipse!

Answer 6

it's either cirlcle or ellips coz parabola only has one variable squared while hyperbola has a minus sign, not + sign. so, i think it's ellips.