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JEE Main 20205 SeptemberEvening Shift
Exam
JEE Main
Year
2020
Date
5 September
Shift
Evening Shift
Subject
Mathematics
Chapter
Circle

JEE Main 2020 · 5 September · Evening Shift · Mathematics · Circle

If the length of the chord of the circle, x ^ 2 + y ^ 2 = r ^ 2 ( r...

If the length of the chord of the circle, x2+y2=r2(r>0){x}^{2} + {y}^{2} = {r}^{2} ( r > 0 ) along the line, y−2x=3y - 2x = 3 is rr, then r2{r}^{2} is equal to:If the length of the chord of the circle, x ^ 2 + y ^ 2 = r ^ 2 ( r > 0 ) along the line, y - 2x = 3 is r , then r ^ 2

Options

  1. A95\dfrac{9}{5}
  2. B1212
  3. C245\dfrac{24}{5}
  4. D125\dfrac{12}{5}

Correct answer

D. 125\dfrac{12}{5}

Step-by-step solution

AB=r,AD=r2AB = r, AD = \dfrac{r}{2}

If the length of the chord of the circle, x ^ 2 + y ^ 2 = r ^ 2 ( r > 0 ) along the line, y - 2x = 3 is r , then r ^ 2

CD=rsin60°=3r2CD = rsin60 ° = \dfrac{\sqrt{3}r}{2}
⇒∣0+0−3∣12+22=3r2⇒r=235⇒r2=125⇒ \dfrac{\left|0 + 0 - 3\right|}{\sqrt{{1}^{2} + {2}^{2}}} = \dfrac{\sqrt{3}r}{2} ⇒ r = 2\sqrt{\dfrac{3}{5}} ⇒ {r}^{2} = \dfrac{12}{5}

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