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Engineering
122 Views   |

A straight line through the point $\dpi{100} A(3,4)$ is such that its intercept between the axes is bisected at $\dpi{100} A$ . Its equation is,

• Option 1)

$x+y=7$

• Option 2)

$3x-4y+7=0$

• Option 3)

$4x+3y=24$

• Option 4)

$3x+4y=25$

As we learnt in Intercept form of a straight line -   - wherein and are the -intercept and -intercept respectively.                a = 6         b = 8 Option 1) This is incorrect option Option 2) This is incorrect option Option 3) This is correct option Option 4) This is incorrect option
Engineering
141 Views   |

The locus of the vertices of the family of parabolas $\dpi{100} y=\frac{a^{3}x^{2}}{3}+\frac{a^{2}x}{2}-2a\; \; is$

• Option 1)

$xy=\frac{105}{64}$

• Option 2)

$xy=\frac{3}{4}$

• Option 3)

$xy=\frac{35}{16}$

• Option 4)

$xy=\frac{64}{105}$

As we learnt in  Rectangular Hyperbola - - wherein    and Standard equation of parabola - - wherein    Family of parabolas For quadratic, A2x2+Bx + C vertex is  so, Eliminating a from h and k Option 1) This is correct option Option 2) This is incorrect option Option 3) This is incorrect option Option 4) This is incorrect option
Engineering
155 Views   |

In an ellipse, the distance between its focii is 6 and minor axis is 8. Then its eccentricity is,

• Option 1)

3/5

• Option 2)

1/2

• Option 3)

4/5

• Option 4)

1/$\dpi{80} \sqrt{5}$

As we learnt in  Coordinates of foci - - wherein For the ellipse       Length of major axis - - wherein Semi minor axis     Eccentricity - - wherein For the ellipse   Distance between its focii is 6.  2ae = 6; ae = 3 minor axis, 2b = 8; b=4 b2 = a2(1-e2) b2 = a2- a2e2 a2=25  a=5   Option 1) 3/5 this is correct option Option 2) 1/2 this is incorrect option Option 3) 4/5 this is...
Engineering
104 Views   |

If the lines $\dpi{100} 3x-4y-7=0\; and\; 2x-3y-5=0\;$  are two diameters of a circle of area $\dpi{100} 49\pi$  square units, then the equation of the circle is

• Option 1)

$x^{2}+y^{2}+2x-2y-47=0$

• Option 2)

$x^{2}+y^{2}+2x-2y-62=0$

• Option 3)

$x^{2}+y^{2}-2x+2y-62=0$

• Option 4)

$x^{2}+y^{2}-2x+2y-47=0$

As we learnt in  General form of a circle -   - wherein centre = radius =    Point of intersection of 3x - 4y - 7= 0 and 2x - 2y - 5 = 0 is (1, -1) which is the center and r = 7 Equation is x2 + y2 - 2x + 2y - 47 = 0. Option 1) this is incorrect Option 2) this is incorrect Option 3) this is incorrect Option 4) this is correct
Engineering
119 Views   |

Let $\dpi{100} C$ be the circle with centre (0, 0) and radius 3 units. The equation of the locus of the mid points of chord of the circle $\dpi{100} C$        that subtend an angle of  $\dpi{100} 2\pi /3$  at its centre is

• Option 1)

$x^{2}+y^{2}=\frac{3}{2}$

• Option 2)

$x^{2}+y^{2}=1$

• Option 3)

$x^{2}+y^{2}=\frac{27}{4}$

• Option 4)

$x^{2}+y^{2}=\frac{9}{4}$

As we learnt in  Equation of a circle - - wherein Circle with centre and radius .  In h2 + k2 = 9/4 Option 1) This is incorrect option Option 2) This is incorrect option Option 3) This is incorrect option Option 4) This is correct option
Engineering
116 Views   |

If $\dpi{100} (a,a^{2})$   falls inside the angle made by the lines $\dpi{100} y=\frac{x}{2},x> 0\; and \, y=3x,x> 0,\; then\; a$ belongs to

• Option 1)

$\left ( 0,\; \frac{1}{2} \right )\;$

• Option 2)

$\; (3,\infty )\;$

• Option 3)

$\; \left ( \frac{1}{2},\; 3 \right )\;$

• Option 4)

$\; \left ( -3,\; -\frac{1}{2} \right )\;$

As we learnt in  Slope of a line - - wherein Slope of line joining A(x1,y1) and  B(x2,y2) . Slope of now  slop of    is    Slop of y=3x is m=3 Thus        Option 1) Incorrect option Option 2) Incorrect option Option 3) Correct option Option 4) Incorrect option
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