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If the line y=m x+1 is tangent to the pa...

If the line `y=m x+1` is tangent to the parabola `y^2=4x ,` then find the value of `mdot`

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To solve the problem, we need to find the value of \( m \) such that the line \( y = mx + 1 \) is tangent to the parabola \( y^2 = 4x \). ### Step 1: Write the equation of the line and the parabola The equation of the line is given as: \[ y = mx + 1 \] The equation of the parabola is: ...
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RD SHARMA ENGLISH-PARABOLA-All Questions
  1. If the line l x+m y+n=0 touches the parabola y^2=4a x , prove that ln=...

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  2. Find the equation of the parabola whose latus-rectum is 4u n i t s , a...

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  3. If the line y=m x+1 is tangent to the parabola y^2=4x , then find the ...

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  4. Find the vertex, focus, directrix, axis and latus-rectum of the par...

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  5. Find the vertex, axis, focus, directrix, latus-rectum of the followi...

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  6. Find the equation of the parabola whose focus is (1,-1) and whose vert...

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  7. Find the equation of the parabola with vertex (2,-3)a n dfoc u s(0,5)d...

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  8. Find the equation of the parabola whose focus is (-3,2) and the direct...

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  9. Find the equation of the lines joining the vertex of the parabola y...

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  10. For the following parabola find the coordinates of the foci, the equ...

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  11. Find the equation of the parabola whose focus is the point (0,0) an...

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  12. Find the area of the triangle formed by the lines joining the vertex...

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  13. Find the coordinates of points on the parabola y^2=8x whose focal dist...

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  14. Find the length of the line segment joining the vertex of the parab...

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  15. Find the equation of the parabola whose focus is(1,1) and equation of ...

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  16. Find the equation of the parabola with vertex is at (2,1) and the dire...

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  17. The focal distance of a point on the parabola y^2=12 x is 4.Find the ...

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  18. Find the equation of the parabola whose focus is at (-1,-2) and the ...

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  19. Find the vertex, focus and directrix of the parabola (4y^2+12x-20y+6...

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  20. Find the angle made by a double ordinate of length 8a at the vertex of...

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