Advertisements
Advertisements
प्रश्न
The shortest distance from the point (2, –7) to the circle x2 + y2 – 14x – 10y – 151 = 0 is equal to 5.
पर्याय
True
False
Advertisements
उत्तर
This statement is False.
Explanation:
Given equation of circle is x2 + y2 – 14x – 10y – 151 = 0
Shortest distance = distance between the point (2, – 7)
And the centre – radius of the circle
Centre of the given circle is
2g = – 14 ⇒ g = – 7
2f = – 10 ⇒ f = – 5
∴ Centre = (– g, – f) = (7, 5)
And r = `sqrt((-7)^2 + (-5)^2 + 151)`
= `sqrt(49 + 25 + 151)`
= `sqrt(225)`
= 15
∴ Shortest distance = `sqrt((7 - 2)^2 + (5 + 7)^2) - 15`
= `sqrt(25 + 144) - 15`
= 13 – 15
= |– 2|
= 2
APPEARS IN
संबंधित प्रश्न
Find the coordinates of the foci, the vertices, the length of major axis, the minor axis, the eccentricity and the length of the latus rectum of the ellipse.
`x^2/36 + y^2/16 = 1`
Find the coordinates of the foci, the vertices, the length of major axis, the minor axis, the eccentricity and the length of the latus rectum of the ellipse.
`x^2/16 + y^2/9 = 1`
Find the coordinates of the foci, the vertices, the length of major axis, the minor axis, the eccentricity and the length of the latus rectum of the ellipse.
`x^2/25 + y^2/100 = 1`
Find the coordinates of the foci, the vertices, the length of major axis, the minor axis, the eccentricity and the length of the latus rectum of the ellipse.
`x^2/100 + y^2/400 = 1`
Find the coordinates of the foci, the vertices, the length of major axis, the minor axis, the eccentricity and the length of the latus rectum of the ellipse.
36x2 + 4y2 = 144
Find the coordinates of the foci, the vertices, the length of major axis, the minor axis, the eccentricity and the length of the latus rectum of the ellipse.
16x2 + y2 = 16
An arch is in the form of a semi-ellipse. It is 8 m wide and 2 m high at the centre. Find the height of the arch at a point 1.5 m from one end.
Find the vertex, focus, axis, directrix and latus-rectum of the following parabola
y2 − 4y + 4x = 0
Find the vertex, focus, axis, directrix and latus-rectum of the following parabola
y2 + 4x + 4y − 3 = 0
Find the vertex, focus, axis, directrix and latus-rectum of the following parabola
y2 = 8x + 8y
Find the vertex, focus, axis, directrix and latus-rectum of the following parabola
4 (y − 1)2 = − 7 (x − 3)
Find the vertex, focus, axis, directrix and latus-rectum of the following parabola
y2 = 5x − 4y − 9
Find the vertex, focus, axis, directrix and latus-rectum of the following parabola
x2 + y = 6x − 14
Write the distance between the vertex and focus of the parabola y2 + 6y + 2x + 5 = 0.
Write the length of the chord of the parabola y2 = 4ax which passes through the vertex and is inclined to the axis at \[\frac{\pi}{4}\]
If the coordinates of the vertex and focus of a parabola are (−1, 1) and (2, 3) respectively, then write the equation of its directrix.
In the parabola y2 = 4ax, the length of the chord passing through the vertex and inclined to the axis at π/4 is
Find the centre, the lengths of the axes, eccentricity, foci of the following ellipse:
x2 + 2y2 − 2x + 12y + 10 = 0
Find the centre, the lengths of the axes, eccentricity, foci of the following ellipse:
4x2 + y2 − 8x + 2y + 1 = 0
Find the centre, the lengths of the axes, eccentricity, foci of the following ellipse:
4x2 + 16y2 − 24x − 32y − 12 = 0
Find the centre, the lengths of the axes, eccentricity, foci of the following ellipse:
x2 + 4y2 − 2x = 0
A rod of length 12 m moves with its ends always touching the coordinate axes. Determine the equation of the locus of a point P on the rod, which is 3 cm from the end in contact with x-axis.
Find the equation of the set of all points whose distances from (0, 4) are\[\frac{2}{3}\] of their distances from the line y = 9.
If the lengths of semi-major and semi-minor axes of an ellipse are 2 and \[\sqrt{3}\] and their corresponding equations are y − 5 = 0 and x + 3 = 0, then write the equation of the ellipse.
If the minor axis of an ellipse subtends an equilateral triangle with vertex at one end of major axis, then write the eccentricity of the ellipse.
If a latus rectum of an ellipse subtends a right angle at the centre of the ellipse, then write the eccentricity of the ellipse.
Given the ellipse with equation 9x2 + 25y2 = 225, find the major and minor axes, eccentricity, foci and vertices.
The equation of the ellipse whose centre is at the origin and the x-axis, the major axis, which passes through the points (–3, 1) and (2, –2) is ______.
The equation of the circle which passes through the point (4, 5) and has its centre at (2, 2) is ______.
If the lines 3x – 4y + 4 = 0 and 6x – 8y – 7 = 0 are tangents to a circle, then find the radius of the circle.
