The line l x-m y-n-0 will be a tangent to the circle x2-y2-a2 iffA- n2l2-m2-a2B- n-6C- -2D- a2l2-m2-n2

The correct option is D Line nbsp;y = mx + c is tangent, if c=± a√(1+m^2) Now lx+my+n=0 or y= 1/mx n/m is tangent, if n/m=± a√(1+l/m^2) or n^2=a^2(m^2+l^2 ...

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Standard XII

Mathematics

Length of Tangent and Power of a Point

The line l x+...

Question

The line $l x + m y + n = 0$ will be a tangent to the circle $x^{2} + y^{2} = a^{2}$ iff

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Solution

The correct option is B

Line y = mx + c is tangent, if $c = \pm a \sqrt{1 + m^{2}}$

Now $l x + m y + n = 0$ or $y = - \frac{1}{m} x - \frac{n}{m}$ is tangent, if

$- \frac{n}{m} = \pm a \sqrt{1 + ⟮ \frac{l}{m} ⟯^{2}}$ or $n^{2} = a^{2} (m^{2} + l^{2})$ .

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The line lx+my+n=0 will be a tangent to the circle x2+y2=a2 iff

The correct option is B Line y = mx + c is tangent, if c=±a√1+m2 Now lx+my+n=0 or y=−1mx−nm is tangent, if −nm=±a√1+⟮lm⟯2 or n2=a2(m2+l2).

The line $l x + m y + n = 0$ will be a tangent to the circle $x^{2} + y^{2} = a^{2}$ iff

The correct option is B

Line y = mx + c is tangent, if $c = \pm a \sqrt{1 + m^{2}}$

Now $l x + m y + n = 0$ or $y = - \frac{1}{m} x - \frac{n}{m}$ is tangent, if

$- \frac{n}{m} = \pm a \sqrt{1 + ⟮ \frac{l}{m} ⟯^{2}}$ or $n^{2} = a^{2} (m^{2} + l^{2})$ .