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Given : A circle, `2x^2+""2y^2=""5`and a parabola, `y^2=""4sqrt(5)""x`.Statement - I : An equation of a common tangent to thesecurves is `y="x+"sqrt(5)`Statement - II : If the line, `y=m x+(sqrt(5))/m(m!=0)`is theircommon tangent, then m satisfies `m^4-3m^2+""2""=0.`(1)Statement - I is True; Statement -II is true; Statement-II is not a correct explanation for Statement-I(2)Statement -I is True; Statement -II is False.(3)Statement -I is False; Statement -II is True(4)Statement -I is True; Statement -II is True; Statement-II is a correct explanation for Statement-IA. Statement-1 is True, Statement - 2 is true, Statement-2 is a correct explanation for Statement-1`B. Statement-1 is True, Statement - 2 is true, Statement-2 is not a correct explanation for Statement-7C. Statement-1 is True, Statement - 2 is False.D. Statement-1 is True, Statement - 2 is True. |
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Answer» Correct Answer - B The equation of a tangent to `y^(2)=4sqrt5x` is `y=mx+sqrt5.m` where m is is the slope of the tangent. If it touches the circle `2x^(2)+2y^(2)=5`, then `|(sqrt(5)//m)/(sqrt(1+m^(2)))|=sqrt((5)/(2))` ` implies m sqrt(1+m^(2))=sqrt(2)` `implies m^(4)+m^(2)-2=0` `implies (m^(2)+2)(m^(2)-1)=0` `implies m = +- 1` Substituting these values in `y=x+sqrt5" and "y=-xsqrt5`. Also, values of m satify `m^(4)-3m^(3)+2=0.` Hence, both the statements are true. But, statement II is not a correct explanation of statement-i. |
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