PARABOLA

If the line x+y-1=0 is a tangent to a parabola with focus (1,2) at A and intersects the diretrix at B and tangent at vertex at C,respectively. Then AC*BC is equal to?

AC denotes the length between the points A and C

#Geometry

Easy Math Editor

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`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$

Comments

In any parabola part of tangent between point of contact and directrix subtends right angle at focus.Also foot of perpendicular from focus on any tangent lies on tangent at vertex.Using these two facts we obtain that triangle ASB is right angled and that SC is perpendicular to AB.Using extension of Pythagoras theorem we have AC.BC=square of SC.We can easily calculate SC which is sqrt(2).Hence the answer is 2

Indraneel Mukhopadhyaya - 5 years, 9 months ago

Ans is 2....

Saksham Sachdeva - 3 years, 6 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$