The circle x2 + y2 = 100 after a translation becomes the circle
(x – 10)2 + (y + 10)2 = 100. Find the translation.
Identify the conic and find its characteristics:
(y – 5)2 = 4(5)(x – 3)
Write an equation and graph the conic section:
Ellipse with center at (2, –1), vertices at (–1, –1), (5, –1), and co–vertices at (2, 1), (2, –3).
Hyperbola with center at (1, 2), one focus at (1, 2 + √ 45), one vertex at (1, 5).
Find an equation for the conic section.
Circle with center at (7, 1) and radius 3
Parabola with vertex at (3, –5) and focus at (3, 4)
Ellipse with vertices at (3, –4) and (3, 9) and foci at (3, 0) and (3, 5).
Hyperbola with vertices at (5, –7), (5, 1) and foci at (5, –9), (5, 3)
Tell which conic is defined by the equation
x2 + 6x – y + 5 = 0.
4x2 + y2– 8x – 2y = –1.
y2 – 2x2 + 2x + 2y = 9.
Find the radius and center of x2 – 4x + y2 + 8y + 4 = 0
Find the focus and vertex of y2 – 8y – 20x + 4 = 0. Plot the graph.
Find the focus and vertex of 16x2 + 9y2 – 36y – 128x + 148 = 0. Plot the graph.
Find the focus and vertex of x2 – 16y2 + 64y – 10x + 167 = 0. Plot the graph.
Write the new equation obtained by translating the equation
2 units right and 4 units up.
Determine the equation of a line which is tangent to the circle:
(x + 1)2 + (y – 2)2 = 4
at the point (1, 2).
