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Parametric Form of Tangent: Ellipse

The values of...

Question

The value(s) of $[c]$ for which the line $y = 4 x + c$ touches the curve $x^{2} + 16 y^{2} = 16$ is/are (where $[.]$ represents greatest integer function)

- 16

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- 17

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16

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17

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Solution

The correct options are
B $- 17$
C $16$
Given curve is ellipse with
$a^{2} = 16, b^{2} = 1$
and the slope of the line is $m = 4$
Hence using the tangency condition
$c = \pm \sqrt{a^{2} m^{2} + b^{2}} \Rightarrow c = \pm \sqrt{16 \cdot 16 + 1} = \pm \sqrt{257} ∴ [c] = - 17, 16$

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Parametric Form of Tangent: Ellipse

Standard XII Mathematics

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The value(s) of [c] for which the line y=4x+c touches the curve x2+16y2=16 is/are (where [.] represents greatest integer function)

The correct options are B −17 C 16Given curve is ellipse with a2=16,b2=1 and the slope of the line is m=4 Hence using the tangency condition c=±√a2m2+b2⇒c=±√16⋅16+1=±√257∴[c]=−17,16

The value(s) of $[c]$ for which the line $y = 4 x + c$ touches the curve $x^{2} + 16 y^{2} = 16$ is/are (where $[.]$ represents greatest integer function)

The correct options are
B $- 17$
C $16$
Given curve is ellipse with
$a^{2} = 16, b^{2} = 1$
and the slope of the line is $m = 4$
Hence using the tangency condition
$c = \pm \sqrt{a^{2} m^{2} + b^{2}} \Rightarrow c = \pm \sqrt{16 \cdot 16 + 1} = \pm \sqrt{257} ∴ [c] = - 17, 16$