QuestionWhich type of conic is represented by the equation below? $$-4 x^{2}+25 y^{2}+8 x+150 y+121=0$$
This is an equation of a hyperbola. Write the equation of this conic section in conic form.

Studdy Solution
Rewrite the equation in standard form by isolating the constant:
$$-4(x - 1)^2 + 25(y + 3)^2 = 100$$
Divide the entire equation by 100 to get the standard form of a hyperbola:
$$\frac{(y + 3)^2}{4} - \frac{(x - 1)^2}{25} = 1$$
This is the equation of the hyperbola in standard form.