1. Find, in standard form, the equation of:
(a) The parabola with focus at \( ( 3,5 ) \) and directrix at \( x = - 1 \)
(b) The ellipse with vertices at \( ( 1 , - 1 ) \) and \( ( 7 , - 1 ) \) and foci at \( ( 4 \pm \sqrt { 5 } , - 1 )\)
Pregunta
Answer
(a)
\(p= 3- (- 1)= 4\\2p= 8\)
Center: \((\frac{3- 1}{2},5)= (1,5)\)
\((y- 5)^{2} = 8(x- 1)\)
(b)
\(2a= 7- 1= 6\Rightarrow a= 3\\c= 4+ \sqrt{5} - \frac{7+ 1}{2}= \sqrt{5} \\b= \sqrt{3^{2}- 5 } = 2\)
Center: \((\frac{7+ 1}{2},- 1)= (4,- 1)\)
\(\frac{(x- 4)^{2} }{9} + \frac{(y+ 1)^{2} }{4} = 1\)
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