The type of conic sections for the nondegenerate equations given below. a) 0.1x2+0.6x−1.6=0.2y−0.1y2 b) 2x2−7xy=−y2+4x−2y−1 c) 8x+2y=y2+4

Question

The type of conic sections for the nondegenerate equations given below.  a) 0.1x2+0.6x−1.6=0.2y−0.1y2  b) 2x2−7xy=−y2+4x−2y−1  c) 8x+2y=y2+4

Delorenzoz · Accepted Answer

a) Consider the equation 0.1x2+0.6x−1.6=0.2y−0.1y2 This equation can be written as: 0.1x2+0.1y2+0.6x−0.2y−1.6=0. It is known that the equation is in the form Ax2+Cy2+Dx+Ey+F=0. Here, the coefficient of x2 and y2 are A=0.1 and C=0.1, that is, A=C Therefore, the equation is of a circle. Hence, the conic section of the given equation is a circle. b) Consider the equation 2x2−7xy=−y2+4x−2y−1. This equation can be written as: 2x2−7xy+y2−4x+2y+1=0. This is in the form of Ax2+Bxy+Cy2+Dx+Ey+F=0 Solve for B2−4AC. B2−4AC=(7―−4(2)(1)) =49−8 =41 This implies that B2−4AC&amp;gt;0 Therefore, the equation is of a hyperbola. Hence, the conic section of the given equation is a hyperbola. c) Consider the equation 8x+2y=y2+4. This equation can be written as: −y2+8x+2y−4=0 It is known that the equation is in the form Ax2+Cy+Dx+Ey+F=0 In the given equation, there is no term of x2, which means that A=0, that is, AC=0 Therefore, the equation is of a parabola. Hence, the conic section of the given equation is a parabola.

The type of conic sections for the nondegenerate equations given below. a) 0.1x^{2}+0.6x-1.6=0.2y-0.1y^{2} b) 2x^{2}-7xy=-y^{2}+4x-2y-1

Answered question

Answer & Explanation

New Questions in Integral Calculus