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(b) Determine the slope and intercept on the coordinate axis of the equation 4x - 5y + 20 = 0. linith whether or not each of the following lines are either. +

(b) Determine the slope and intercept on the coordinate axis of the equation 4x - 5y + 20 = 0. linith whether or not each of the following lines are either. +

Holt Mcdougal Larson Pre-algebra: Student Edition 2012
Holt Mcdougal Larson Pre-algebra: Student Edition 2012
1st Edition
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Chapter8: Linear Functions
Section8.4: The Slope Of A Line
Problem 16E
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12:46 Pf < 同 (b) Determine the slope and intercept on the coordinate axis of the equation 4x - 5y + 20 = 0. . (c) With the aid of clear workings, state explicitly whether or not each of the following lines are either parallel, perpendicular, or neither. (1) y = 3x + 2 and y = 3x -2 Tii) 3x - 2y = 5 and 2x + 3y = 4 (ii) x + 3y = 1 and 4x + 2y = 3 3. (a) The tangent and normal to the parabola y² = 20x at the point 7(5.10) meet the x-axis at the point A and 5. Show that AB2= AT2 + TB2 Given the equation of the parabola x² = -50y, find its: (i) vertex, (ii) focus (iii) directrix 4. (a) Show that any line passing through the point (4,-1) cannot be a tangent to the circle x²+²-4x+6y- 12 = 0.Hence deduce the centre and radius of the circle. 22 (b) Find the length of the tangent to the circle x² +y²-3x +2y- 10 = 0 from point (-4,1). (c) Find the equation of the tangent to the circle whose equation is x² + y²+2x-3y - 13 = 0 at point (1.-2). " ) 5. (a) Find an equation of an ellipse with the following conditions: foci (0, 19), length of the minor axis 24. (b) From the equation of an ellipse 2 +9y2 + 4x + 18y-23 = 0, find the coordinate of the following (iii) co-vertices (iv) foci. (i) centre (ii) vertices 6. (a) Given the equation of the hyperbola. 36x² (i)coordinates of the center of the hyperbola (iv) its conjugate axes and the lengths of: its transverse and conjugate axes, (vii) its equations of the directrices and asymptotes. (vi) its eccentricity, (b) Find the equation of the hyperbola whose transverse axis is on the x-axis having asymptotes: y + 2x + 4 5 y-2x-4 and passes through (2, 2). (a) 2 - 4y + 4x = 0 (b) 3x2 + 12x - 8y = 0 (c) 22x12y + 25 =0 (d) y² +4y+20x + 4 =0 e) y² = 16x (f) ² = -9y 19. Find the equation of parabola, given Edit MAL. YAHAYA AJIYA (B.Sc GSU, M.Sc UNILORIN) 16. Find the equation of the tangent to cach circle through the given external point (a) z²+²= 25, (7,1), (b) z²+y²-4x+2y-31 = 0, (-1,5) (c) ²+²= 169, (5,-12), (d) 2² + y²-4x+6y-37= 0, (3, 4). 18. Describe each of the following equations of parabola x² = 49 - 17. Find the length of the tangent to each of the following circles. (a) ²+² +92-11y +48 = 0, (-1,2), (b) x² + y²-2x - 4y -4 = 0, (8,10). F(-2,0) d:x+3=0 A 25y² = 900, Deduce the following: (ii) its vertices (iii) its foci Annotate "... 38 | (a) V(0,0), (b) v (0,0); (c) V(0,0), F(0,5) (d) V(0,0), F on z-axis passes through (-2,6) (e) V(1,3), F(-1,3) T मंत्र म V = (0,0) f = (a,0) d = x=9 L = 49 ■ Fill & Sign Unsifted. J case Y= (0,0) y Eo. 42249 y² = 16 ₂0 4, f=0,9 d=y=-a L = £49 = 16x compare 49 Jasua a=4. : 4410 ~= (010) Convert All
Transcribed Image Text:12:46 Pf < 同 (b) Determine the slope and intercept on the coordinate axis of the equation 4x - 5y + 20 = 0. . (c) With the aid of clear workings, state explicitly whether or not each of the following lines are either parallel, perpendicular, or neither. (1) y = 3x + 2 and y = 3x -2 Tii) 3x - 2y = 5 and 2x + 3y = 4 (ii) x + 3y = 1 and 4x + 2y = 3 3. (a) The tangent and normal to the parabola y² = 20x at the point 7(5.10) meet the x-axis at the point A and 5. Show that AB2= AT2 + TB2 Given the equation of the parabola x² = -50y, find its: (i) vertex, (ii) focus (iii) directrix 4. (a) Show that any line passing through the point (4,-1) cannot be a tangent to the circle x²+²-4x+6y- 12 = 0.Hence deduce the centre and radius of the circle. 22 (b) Find the length of the tangent to the circle x² +y²-3x +2y- 10 = 0 from point (-4,1). (c) Find the equation of the tangent to the circle whose equation is x² + y²+2x-3y - 13 = 0 at point (1.-2). " ) 5. (a) Find an equation of an ellipse with the following conditions: foci (0, 19), length of the minor axis 24. (b) From the equation of an ellipse 2 +9y2 + 4x + 18y-23 = 0, find the coordinate of the following (iii) co-vertices (iv) foci. (i) centre (ii) vertices 6. (a) Given the equation of the hyperbola. 36x² (i)coordinates of the center of the hyperbola (iv) its conjugate axes and the lengths of: its transverse and conjugate axes, (vii) its equations of the directrices and asymptotes. (vi) its eccentricity, (b) Find the equation of the hyperbola whose transverse axis is on the x-axis having asymptotes: y + 2x + 4 5 y-2x-4 and passes through (2, 2). (a) 2 - 4y + 4x = 0 (b) 3x2 + 12x - 8y = 0 (c) 22x12y + 25 =0 (d) y² +4y+20x + 4 =0 e) y² = 16x (f) ² = -9y 19. Find the equation of parabola, given Edit MAL. YAHAYA AJIYA (B.Sc GSU, M.Sc UNILORIN) 16. Find the equation of the tangent to cach circle through the given external point (a) z²+²= 25, (7,1), (b) z²+y²-4x+2y-31 = 0, (-1,5) (c) ²+²= 169, (5,-12), (d) 2² + y²-4x+6y-37= 0, (3, 4). 18. Describe each of the following equations of parabola x² = 49 - 17. Find the length of the tangent to each of the following circles. (a) ²+² +92-11y +48 = 0, (-1,2), (b) x² + y²-2x - 4y -4 = 0, (8,10). F(-2,0) d:x+3=0 A 25y² = 900, Deduce the following: (ii) its vertices (iii) its foci Annotate "... 38 | (a) V(0,0), (b) v (0,0); (c) V(0,0), F(0,5) (d) V(0,0), F on z-axis passes through (-2,6) (e) V(1,3), F(-1,3) T मंत्र म V = (0,0) f = (a,0) d = x=9 L = 49 ■ Fill & Sign Unsifted. J case Y= (0,0) y Eo. 42249 y² = 16 ₂0 4, f=0,9 d=y=-a L = £49 = 16x compare 49 Jasua a=4. : 4410 ~= (010) Convert All
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