## Related questions with answers

The telescope at the Palomar Observatory in California has a parabolic mirror. The circle at the top of the parabolic mirror has a 200-inch diameter. An equation that approximates the parabolic cross-section of the surface of the mirror is

$y = \frac { 1 } { 2639 } x ^ { 2 }$

, where x and y are measured in inches. How far is the focus from the vertex of the mirror? If a point on a parabola whose vertex is at the origin is known, then the equation of the parabola can be found. For instance, if (4, 1) is a point on a parabola with vertex at the origin, then we can find the equation as follows:

$y = \frac { 1 } { 4 p } x ^ { 2 }$

\cdot

$Begin with the general form of the equation of a parabola.$

1 = $\frac { 1 } { 4 p }$ ( 4 ) ^ { 2 }\cdot

$The known point is (4, 1). Replace x by 4 and y by 1.$

1 = $\frac { 4 } { p }$\cdot

$Solve for p. p=4$

\cdot

$p=4 in the equation$

y = $\frac { 1 } { 4 p }$ x ^ { 2 }

$. The equation of the parabola is$

y = $\frac { 1 } { 16 }$ x ^ { 2 }

$.$

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