If a hyperbola is passing through (3,2) and (-17,12), having its vertices, origin and its transverse axis on the x-axis, then the length of the transverse axis is -
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Among the following a line passing through origin is (x, y ≠ 0)
Correct option is (C) y = 3x \(y=3x\) is line passing through origin. (Because (0, 0) satisfies the equation y = 3x)
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Among the following a line passing through origin is (x, y ≠ 0)
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The graph of x = k is a line parallel to Y – axis at a distance of k units and passing through the point
Correct option is (C) (k, 0) Line x = k is passing through the point (k, 0).
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The graph of x = k is a line parallel to Y – axis at a distance of k units and passing through the point
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The graph of y = k is a line parallel to X – axis at a distance of k units and passing through the point
Correct option is (D) (0, k) Line y = k is passing through the point (0, k).
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The graph of y = k is a line parallel to X – axis at a distance of k units and passing through the point
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Vertical axis and horizontal axis are A) x – axis, y – axis
B) y – axis, x – axis
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Graph of Hooke’s law is in the shape of A) straight line passing through origin
A) straight line passing through origin
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Example 13 Find the equation' of the ellipse, with major axis along the \( x \)-axis ax passing through the points \( (4,3) \) and \( (-1,4) \).
Let the equation of ellipse be \(\frac{x^2}{a^2}\) + \(\frac{y^2}{b^2}\) = 1 ....(1) Ellipse is passing through points (4,3) & (-1,4) and major axis be x-axis. ∴ \(\frac{16}{a^2}\) + \(\frac{9}{b^2}\) = 1 ....(2) \(\frac{1}{a^2}\) + \(\frac{16}{b^2}\) = 1 ....(3) Multiplying equation (3) by 16,we get \(\frac{16}{a^2}\) + \(\frac{256}{b^2}\) = 16...
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Let a hyperbola passes through the focus of the ellipse `(x^(2))/(25)-(y^(2))/(16)=1`. The transverse and conjugate axes of this hyperbola coincide wi
For the given ellipse, `(x^(2))/(25)+(y^(2))/(16)=1, e=sqrt(1-(16)/(25))=(3)/(5)`. So, eccentricity of hyperbola `=(5)/(3)`. Let the hyperbola be, `(x^(2))/(A^(2))-(y^(2))/(B^(2))=1 " " ...(1)` Then, `B^(2)=A^(2)((25)/(9)-1)=(16)/(9)A^(2)`. Also, foci of ellipse are `(+-3,0)`. As, hyperbola passes...
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