Use the points A(-1,2,4),B(0,6,-3), and C(2,-4,1). Write parametric equations for the line through C and the midpoint of AB.

The equation r=a(1-e²)/(1+e cos θ) yields no true parabolas. Justify your answer.

Prove that the graph of the equation is an ellipse, and find its vertices, foci, and eccentricity.

$$3x^2+5y^2-12x+30y+42=0$$

Use the discriminant B²-4AC to decide whether the equation represents a parabola, an ellipse , or a hyperbola.

$$9x^2-6xy+y^2-7x+5y=0$$

Use the points A(-1,2,4),B(0,6,-3),and C(2,-4,1). Write parametric equations for the line through B and the midpoint of AC.

True or False The equation r=a(1-e²)/(1+e cos θ) yields no true parabolas. Justify your answer.

Graph the parabola using a function grapher.

$$(y+2)^2=-8(x+1)$$

Graph the hyperbola using a parametric grapher in Dot graphing mode.

$$\dfrac{(x+3)^2}{12}-\dfrac{(y-6)^2}{5}=1$$

Use the discriminant $B^2 - 4AC$ to decide whether the equation represents a parabola, an ellipse, or a hyperbola. $9 x^{2}-6 x+y^{2}-7 x+5 y=0$

Find the equation for the conic in standard form. Hyperbola: center (0,0), foci (0,±6), vertices( 0,±5).

Prove that the graph of the equation is an ellipse, and find its vertices, foci, and eccentricity.

$$9x^2+4y^2-18x+8y-23=0$$

Use the points A(-1,2,4),B(0,6,-3), and C(2,-4,1). Write parametric equations for the line through B and C.

Use the discriminant $B^2 - 4AC$ to decide whether the equation represents a parabola, an ellipse, or a hyperbola. $x^{2}-4 x+3 x+25 y-6=0$

Use the discriminant B²-4AC to decide whether the equation represents a parabola, an ellipse, or a hyperbola. x²-4xy+3x+25y-6=0.