Length of the chord joining the points P- and Q- on the circle x2-y2-a2 is

The correct option is A 2a sin(α β2) In right angled triangle ROQ (O origin), sin(α β2) = RQOQ ⇒ RQ = a sin(α β2) #16 ...

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Standard X

Mathematics

Chord Properties of Circles

Length of the...

Question

Length of the chord joining the points $P (α)$ and $Q (β)$ on the circle $x^{2} + y^{2} = a^{2}$ is

2 a cos (\frac{α - β}{2})

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2 a sin (\frac{α - β}{2})

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2 a tan (\frac{α - β}{2})

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2 a csc (\frac{α - β}{2})

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Solution

The correct option is A $2 a sin (\frac{α - β}{2})$
In right - angled triangle ROQ (O-origin),

$s i n (\frac{α - β}{2})$ = $\frac{R Q}{O Q}$

$\Rightarrow$ $R Q$ = $a s i n (\frac{α - β}{2})$ (Since, $O Q$ is the radius of the given circle)

$∴$ Length of chord = $2 R Q$ = $2 a s i n (\frac{α - β}{2})$

So, the correct option is 'B'.

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Similar questions

The equation of chord joining 2 point P $(α)$ and Q $(β)$ in a hyperbola $\frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} = 1 i s \frac{x}{a} . c o s (\frac{α - β}{2}) - \frac{y}{b} . s i n (\frac{α + β}{2}) = c o s [\frac{α + β}{2}]$ .

Q. If

α + β = 3 π

then the chord joining the points

α

and

β

for the hyperbola

\frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} = 1

passes through

Q. The point of intersection of the tangents drawn at the ends of the chord joining the points

α

and

β

on the circle

x^{2} + y^{2} = a^{2}

Q. The point of intersection of tangents to the ellipse

\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1

at two points

the sum of whose eccentric angles is constant, is

(a \frac{c o s \frac{α + β}{2}}{c o s \frac{α - β}{2}}, b \frac{s i n \frac{α + β}{2}}{c o s \frac{α - β}{2}})

A circle with centre at the origin and radius equal to a meets the axis of x and A and B. $P (α)$ and $Q (β)$ are two points on this circle so that $α - β = 2 γ$ , where $γ$ is a constant. The locus of the point of intersection of AP and BQ is

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Length of the chord joining the points P(α) and Q(β) on the circle x2+y2=a2 is

The correct option is A 2asin(α−β2)In right - angled triangle ROQ (O-origin),sin(α−β2) = RQOQ⇒ RQ = asin(α−β2) (Since, OQ is the radius of the given circle)∴ Length of chord = 2RQ = 2asin(α−β2) So, the correct option is 'B'.

Length of the chord joining the points $P (α)$ and $Q (β)$ on the circle $x^{2} + y^{2} = a^{2}$ is