Question

DI y the 'arabolas Exercises 12.3 Complete the following: tant for that one Conics also ex oint where the parede ertex, the direction nd the focus is always ocus are called focal cases xis of symmetry is atus rectum are a Turvature of any como ind points in a parabole 1. Complete the squares for each quadratic, list the center and radius, then graph each circle A characteristici: 's the locus of points we the focus and an r= -5 = 15 Since the radius is an imaginary value, the equation is not a real circle. labeling its translated center: la) x² + 2x + y2 – 4y = 4 (b) x² + y2 - 4x = 0 and distance to do (c) 2x2 + 2y2 + 3x - 5y = 2 (d) x² + y² - 2x - 8y=8 (e) x2 + y2 + 3x = 4 (6) 4x² + 4y² – 16x + 24y=-27 (h) x² + y² -7y=0 (g) x2 + y2 + 4x = 0 () x² + y2 - 2ax + 2by =C always equals ome. The quation. From the ecer ocus the directrix. O Select any point Ligure 12D). Sir

Answer 1

X^2 + Y^2 + 2mX - 2nY = 0

Then ,complete squares for X and Y by adding m,n terms

Write

( X^2 + 2mX + A ) + (Y^2 - 2nY + B ) = 0 + A + B

Now

(X^2 + 2mX + m^2 ) + (Y^2 -2nY + n^2) = 0 + m^2 + n^2

( X + m)^2 + ( Y - n )^2 = m^2 + n^2

THEN Answer IS

Center of circle is at = ( -m, n)

Radius R is = √m^2 + n^2

NOW graph this circle