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Exercises (1) Find the points of intersection of the parabola \( y^{2}=4 x \) and the circle \( 4 x^{2}+4 y^{2}-25 x+y+3=0 \). (2) Find the equations of the tangents from the point \( (4,4) \) to the hyperbola \( 9 \mathrm{x}^{2}-9 \mathrm{y}^{2}=16 \). (3) Find the points of intersection of the line \( y=m x+c \) and the parabola \( y^{2}=4 a x \). (4) Find the equations of the two tangents that can be drawn from the point \( (2,3) \) to the parabola \( \mathrm{y}^{2}=4 \mathrm{ax} \) when \( \mathrm{a}=1 \).

          Exercises
(1) Find the points of intersection of the parabola \( y^{2}=4 x \) and the circle \( 4 x^{2}+4 y^{2}-25 x+y+3=0 \).
(2) Find the equations of the tangents from the point \( (4,4) \) to the hyperbola \( 9 \mathrm{x}^{2}-9 \mathrm{y}^{2}=16 \).
(3) Find the points of intersection of the line \( y=m x+c \) and the parabola \( y^{2}=4 a x \).
(4) Find the equations of the two tangents that can be drawn from the point \( (2,3) \) to the parabola \( \mathrm{y}^{2}=4 \mathrm{ax} \) when \( \mathrm{a}=1 \).

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Exercises
(1) Find the points of intersection of the parabola y^2=4 x and the circle 4 x^2+4 y^2-25 x+y+3=0.
(2) Find the equations of the tangents from the point (4,4) to the hyperbola 9 x^2-9 y^2=16.
(3) Find the points of intersection of the line y=m x+c and the parabola y^2=4 a x.
(4) Find the equations of the two tangents that can be drawn from the point (2,3) to the parabola y^2=4 ax when a=1.

Added by Gregg M.

Precalculus with Limits

Ron Larson 3rd Edition

Chapter 10

Instant Answer

Solved by Expert Daniel Pyda

Step 1

1. Substitute \( y^2 = 4x \) into the circle's equation: \[ 4x^2 + 4(4x) - 25x + y + 3 = 0 \] Simplify to: \[ 4x^2 + 16x - 25x + y + 3 = 0 \] \[ 4x^2 - 9x + y + 3 = 0 \] 2. Substitute \( y = \pm \sqrt{4x} \) into the equation: Show more…

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Exercises (1) Find the points of intersection of the parabola \( y^{2}=4 x \) and the circle \( 4 x^{2}+4 y^{2}-25 x+y+3=0 \). (2) Find the equations of the tangents from the point \( (4,4) \) to the hyperbola \( 9 \mathrm{x}^{2}-9 \mathrm{y}^{2}=16 \). (3) Find the points of intersection of the line \( y=m x+c \) and the parabola \( y^{2}=4 a x \). (4) Find the equations of the two tangents that can be drawn from the point \( (2,3) \) to the parabola \( \mathrm{y}^{2}=4 \mathrm{ax} \) when \( \mathrm{a}=1 \).

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