If the lines <math> <mrow> <mn>3</mn> <mi>x</mi> <mo>−</mo> <mn>4</mn> <mi>y</mi> <mo>+</mo> <mn>4</mn> <mo>=</mo> <mn>0</mn> </mrow> </math> and <math> <mrow> <mn>6</mn> <mi>x</mi> <mo>−</mo> <mn>8</mn> <mi>y</mi> <mo>−</mo> <mn>7</mn> <mo>=</mo> <mn>0</mn> </mrow> </math> are tangents to a circle, then find the radius of the circle. [Hint: Distance between given parallel lines gives the diameter of the circle.]

This is a Short Answer Type Questions as classified in NCERT ExemplarSol: Sol:Given equation are 3x−4y+4=0and 6x−8y−7=0 ⇒3x−4y−72=0Since 36=−4−8=12 then the lines are parallel.So, the between the parallel lines=|c1−c2a2+b2|=|4+72(3)2+(−4)2| =|1525|=32 Diameter=32∴ Radius=34Hence, the required radius=34.

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Maths Class 11th Conic Sections Exemplar Solution Maths NCERT Exemplar Solutions Class 11th Chapter Eleven

If the lines $3 x - 4 y + 4 = 0$ and $6 x - 8 y - 7 = 0$ are tangents to a circle, then find the radius of the circle.
[Hint: Distance between given parallel lines gives the diameter of the circle.]

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alok kumar singh | Contributor-Level 10

2 months ago

This is a Short Answer Type Questions as classified in NCERT Exemplar

Sol:

Sol:

$G i v e n e q u a t i o n a r e 3 x - 4 y + 4 = 0 a n d 6 x - 8 y - 7 = 0 \Rightarrow 3 x - 4 y - \frac{7}{2} = 0$
$\begin{array}{l} Since \frac{3}{6} = \frac{- 4}{- 8} = \frac{1}{2} t h e n t h e l i n e s a r e p a r a l l e l . \\ S o, t h e b e t w e e n t h e p a r a l l e l l i n e s = | \frac{c_{1} - c_{2}}{\sqrt[]{a^{2} + b^{2}}} | = | \frac{4 + \frac{7}{2}}{\sqrt[]{{(3)}^{2} + {(- 4)}^{2}}} | \\ = | \frac{\frac{15}{2}}{5} | = \frac{3}{2} \\ D i a m e t e r = \frac{3}{2} \\ ∴ R a d i u s = \frac{3}{4} \\ H e n c e, t h e r e q u i r e d r a d i u s = \frac{3}{4} . \end{array}$

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If the lines $3 x - 4 y + 4 = 0$ and $6 x - 8 y - 7 = 0$ are tangents to a circle, then find the radius of the circle.
[Hint: Distance between given parallel lines gives the diameter of the circle.]

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If the lines 3 x − 4 y + 4 = 0 and 6 x − 8 y − 7 = 0 are tangents to a circle, then find the radius of the circle.[Hint: Distance between given parallel lines gives the diameter of the circle.]

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If the lines $3 x - 4 y + 4 = 0$ and $6 x - 8 y - 7 = 0$ are tangents to a circle, then find the radius of the circle.
[Hint: Distance between given parallel lines gives the diameter of the circle.]