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Prove that if a plane has the intercepts a, b, c and is at a distance of p units from the origin, then $$1/a^2 + 1/b^2 + 1/c^2 = 1/p^2$$
cbse
class12
bookproblem
sec-c
difficult
math
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asked
Nov 2, 2012
by
balaji.thirumalai
retagged
Mar 19, 2014
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Prove that if a plane has the intercepts $a, b, c$ and is at a distance of $p$ units from the origin, then $\large\frac{1}{a^2}+\frac{1}{b^2}+\frac{1}{c^2} = \frac{1}{p^2}$.
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Nov 29, 2012
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1
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If $p$ is the length of perpendicular from the origin to the line whose intercepts on the axes are $a$ and $b$, then show that $ \large\frac{1}{p^2}$$= \large\frac{1}{a^2}$$ +\large\frac{1}{b^2}$
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A variable plane, which remains at a constant distance '3p' from the origin cuts the coordinate axes at A, B and C. Show that locus of the centroid of the triangle is \(\large \frac{1}{x^2} + \frac{1}{y^2} + \frac{1}{z^2} = \frac{1}{p^2} .\)
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If $p$ and $q$ are the lengths of perpendiculars from the origin to the lines $ x \cos \theta - y \sin \theta = k \cos 2\theta$ and $ x \sec \theta + y \: cosec \theta -k$, respectively, prove that $ p^2+4q^2=k^2$
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If $a$ and $b$ are roots of $x^2-3x+p=0$ and $c$ and $d$ are roots of $x^2-12x+q=0$, where $a,b,c,d$ form a G.P. then prove that $(q+p):(q-p)=17:15$
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Find the direction in which a straight line must be drawn through the point (–1, 2) so that its point of intersection with the line $ x + y = 4$ may be at a distance of 3 units from this point
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The relation \(R\) in the set \(A\) of points in a plane given by \(R = \{(P, Q)\) : distance of the point \(P\) from the origin is same as the distance of the point \(Q\) from the origin\(\}\), is a) Reflexive only b) Symmetry C) both reflexive and symmetry but not transitive d) Is an equivalence relation. Also show that the set of all points related to a point Pis not equal to (0,0) is the circle passing through P with origin as centre.
cl121
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asked
Jun 12, 2014
by
balaji.thirumalai
1
answer
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