JDM chap 4 Conic

Unit Matematik
Kolej Matrikulasi Johor
Kementerian Pendidikan Malaysia
JOM-DO-MATHS ( JDM)
Chapter 4 :Conics ( Set 1 )

1. Find the center and the length of the radius of each of the circles.

(a) x  32  y  22  25
(b) y  42  x  22  2

(c) x2  y2  6x 10y  30  0
(d) 4x2  4y2  4x  8y 11  0

2. A circle with centre 4,2 passes through the point 10,6 and a,8. Find

(i) the value of a.
(ii) the general equation of the circle.

3. Find the equation of tangent lines from the point 1, 3to the circle x2  y2 1.

4. (a) Find an equation of the circle that passes through the point A 0,1, B4,1 and C 1, 2.

(b) Find the points of intersection between the circle obtained in part (a) and the circle
x2  y2  2y  3.

5. Find the equations of the tangents to the following circles at the points given.

(a) x2  y2  2x  6y  8  0 , at 2,2
(b) x2  y2  8x  2y 15  0 , at 3,2

6. Find the lengths of the tangents from given points to the given circles. Page 1
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(a) 3, 5 ; x2  y2  2x  4y  4  0
(b)  2, -1; 3x2  3y2  2x  y  7  0

7. Determine the coordinates of the center and the radius of the circle with equation

x2  y2  2x  6y  26  0 .Find the distance from the point P7,9 to the center of the

circle. Hence find the length of the tangents from P to the circle.

8. A circle passes through the points A 2, 4 , B7, 7 and the centre lies on the line

y  x 1. Find the radius and standard equation of the circle.

9. Given the circles
C1 : x2  y2 10x 18y  70  0
C2 : x2  y2  6y  7  0

Find the centers and radius of both circles, and hence show that these two circles do not
touch each other. Determine the shortest distance between them.

10. A circle touches the line x  y  3 at point (1,6) and its centre lies on a straight line
5x  2y  2 .

(a) Find the point of intersection between the normal to the circle at (1,6) and the straight
line 5x  2y  2 .

(b) Hence, determine the centre, radius and general equation of circle.

11. The lines  x  2y  7  0 and 3x  y  0 intersect at P. Page 2
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(a) Find the coordinate of P.

(b) Find the general equation for the circles which touches the line 3x  y  0 at P and
has the center lying on the line x  y  0 .

(c) Show that the point 10, 7 is located outside the circle. Hence find the length of
tangent to the circle from the point 10, 7 .

12. A circle touches the line 5y 12x  59 at the point (7,5) and has its centre on
the line y  7 x  5 .
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(a) Determine the general equation of this circle.
(b) Find the equation of the tangent which is parallel to the tangent at the point (7,5) .
(c) Find the length of tangent to the circle from the point (6 , 8) .

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Unit Matematik
Kolej Matrikulasi Johor
Kementerian Pendidikan Malaysia
JOM-DO-MATHS( JDM)
Chapter 4 :Conics ( Set 2 )

1. Find the vertices, foci and center for the ellipses.

(a) x2  y2  1 (b) 100x2  4y 2  25
25 4

(c) (x 1)2  ( y  2)2  1 (d) 4(x  2)2  ( y  2)2 16
94

2. Determine the equation of the ellipse if given

(a) center at 0, 0, focus at 5, 0; vertex at 7, 0 .
b) foci at 3,  3 and length of major axis is 10.
c) vertices at  6,  3 and 10,  3 , c  5.

3. Show that the following equations represents an ellipse .Find the coordinates of center,
vertices, foci and the length of major and minor axis. Hence, sketch the graph.
(a) x2  4x  4y2  0
(b) 4x2  9y 2  24x  36y  36
(c) y2  9x2 18x  6y  0
(d) 9x2  54x  47  4y 2 16y

4. Given the foci of an ellipse are ( –1,6 ) and (–1,0 ),with the length of the major axis is 10
units. Find the equation of the ellipse and hence, sketch the graph.

5. Show that the equation 16x2  4y2  64x  40y 100  0 represents an ellipse. Find the
centre, foci and vertices of the ellipse.

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Unit Matematik
Kolej Matrikulasi Johor
Kementerian Pendidikan Malaysia
JOM-DO-MATHS (JDM)
Chapter 4 :Conics ( Set 3 )

1. . Sketch the following parabolas showing clearly the focus and directrix of each one.

a) ( y  2)2  4(x  3) b) ( y  2)2  8(x 1)

c) (x  2)2  12( y 1) d) x2  8x  8y  8

2. Find the equation of a parabola in Cartesian form whose focus, F and vertex,V are given
below:

a) F(7,2) , V (5,2) b) F(3,5) , V (3,1)

c) F(4,1) , V (1,1)

3. Find the equation of the parabolas with vertex (0,0) that satisfy the given conditions:

a) directrix x  4  0 b) focus F0,3

c) open upward and through passing the point 3,4

4. Express the equation of parabola x2  4x  24y  76  0 in standard form.
Hence, determine the coordinates of its vertex and focus.

5. The equation of a parabola is given by y2  4x  8y  8  0. Find the vertex, the focus
and the directrix, and sketch its graph.

6. Find the equation of a parabola, whose axis of symmetry is parallel to y  axis and has

vertex at  3,  4  and passes through 10,3 . Hence, sketch the graph and label vertex

and its focus.

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