Question

Question 15 O pts Each equation below represents a conic section. Write the name of the corresponding type of conic. Explain how you know if it is a circle, ellipse, hyperbola or parabola. a) 1 25 9 b) y2 + 6y + x - 6 = 0 c) x² + y2 100

Answer 1

Solution-

(a)

Consider the equation

$\frac{x^2}{25}-\frac{y^2}{9}=1$

This is the equation of hyperbola because it contains both x² and y² terms and the minus (–) sign between two terms (x²/25 and y²/9) .

Hence, it is an equation representing hyperbola because of presence both x² and y² terms and the negative sign between them.

(b)

Consider the equation

y²+ 6y + x - 6 =0

This is the equation of parabola because it contains only one square term (y²) while other non-sqaure terms

Hence, it is an equation representing parabola because of presence only one square term y².

(c)

Consider the equation

x² + y² = 100

This is the equation of circle because it contains both x² and y² terms with same cofficient (1)

Hence, it is an equation representing circle because of presence both x² and y² terms with same cofficient (1).