2x + 87x - 25 = y + 4y is an example of a
a Circle b. parabola c. ellipse
d. hyperbola
Answers
Given : 2x² + 87x - 25 = y² + 4y
To Find : Equation is an example of a
a Circle b. parabola c. ellipse d. hyperbola
Solution:
2x² + 87x - 25 = y² + 4y
=> 2x² + 87x - 25 = (y + 2)² - 4
=> 2(x² + 87x/2) - 21 = (y + 2)²
=> 2( (x + 87/4)² - (87/4)²) - 21 = (y + 2)²
=> 2(x + 87/4)² - 87²/8 - 21 = (y + 2)²
=> > 2(x + 87/4)² - 7737/8 = (y + 2)²
=> 2(x + 87/4)² - (y + 2)² = 7737/8
=> 2(x + 87/4)² / ( 7737/8 ) - (y + 2)²/ ( 7737/8 ) = 1
=> (x + 87/4)² / (7737/16) - (y + 2)²/ ( 7737/8 ) = 1
=> (x - (- 87/4))² / (7737/16) - (y -( 2-))²/ ( 7737/8 ) = 1
=> (x - (- 87/4))² / (√(7737/16))² - (y -( 2-))²/ (√( 7737/8 ))² = 1
Equation is of form
(x - h)²/a² - (y - k)²/b² = 1
Hence HYPERBOLA
2x² + 87x - 25 = y² + 4y is an example of a HYPERBOLA
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