Find the intersection points, x^2+y^2-16y+39=0, y^2-x^2-9=0
1 answer:
X^2 + y^2 - 16y + 39 = 0
<span>-x^2 + y^2 - 9 = 0 </span>
<span>----------------------------------- </span>
<span>2y^2 - 16y + 30 = 0 iff </span>
<span>y^2 - 8y + 15 = 0 iff </span>
<span>(y - 3)(y - 5) = 0 iff </span>
<span>y = 3 or y = 5. </span>
<span>Now plug in y value into any of the given equations (the second one is easier) to find respective x values. </span>
<span>y^2 - x^2 - 9 = 0 </span>
<span>(3)^2 - x^2 - 9 = 0 iff </span>
<span>9 - x^2 - 9 = 0 iff </span>
<span>x^2 = 0 iff </span>
<span>x = 0 </span>
<span>(0, 3) </span>
<span>y^2 - x^2 - 9 = 0 </span>
<span>(5)^2 - x^2 - 9 = 0 iff </span>
<span>25 - x^2 - 9 = 0 iff </span>
<span>16 - x^2 = 0 iff </span>
<span>(4 - x)(4 + x) = 0 iff </span>
<span>x = 4 or x = -4 </span>
<span>(4, 5), (-4, 5) </span>
<span>We have three points of intersection, which are (0, 3), (4, 5), and (-4, 5).</span>
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