If straight line x+y-2=0 touches a parabola at (1.1), with focus at origin, then:
(A) Its directrix passes through (1,3)
(B) Number of such parabolas is 1
(C) Number of such parabolas is 2
(D) Its axis passes through (3,3)
Answers
Answer:
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To work around this problem, manually remove the hidden bookmarks. To do this, follow these steps:
In Microsoft Word 2002 or in Microsoft Office Word 2003, click Bookmarks on the Insert menu.
In Microsoft Office Word 2007, click the Insert tab, and then click Bookmarks in the Links group.
Click to select the Hidden bookmarks check box to view the list of hidden bookmarks.
In the list of bookmarks, click the bookmark that you want to remove, and then click Delete.
Repeat Step 3 for each bookmark that you want to remove.
Click Close.
To work around this problem, manually remove the hidden bookmarks. To do this, follow these steps:
In Microsoft Word 2002 or in Microsoft Office Word 2003, click Bookmarks on the Insert menu.
In Microsoft Office Word 2007, click the Insert tab, and then click Bookmarks in the Links group.
Click to select the Hidden bookmarks check box to view the list of hidden bookmarks.
In the list of bookmarks, click the bookmark that you want to remove, and then click Delete.
Repeat Step 3 for each bookmark that you want to remove.
To work around this problem, manually remove the hidden bookmarks. To do this, follow these steps:
In Microsoft Word 2002 or in Microsoft Office Word 2003, click Bookmarks on the Insert menu.
In Microsoft Office Word 2007, click the Insert tab, and then click Bookmarks in the Links group.
Click to select the Hidden bookmarks check box to view the list of hidden bookmarks.
In the list of bookmarks, click the bookmark that you want to remove, and then click Delete.
Repeat Step 3 for each bookmark that you want to remove.
Click Close.
To work around this problem, manually remove the hidden bookmarks. To do this, follow these steps:
In Microsoft Word 2002 or in Microsoft Office Word 2003, click Bookmarks on the Insert menu.
In Microsoft Office Word 2007, click the Insert tab, and then click Bookmarks in the Links group.
Click to select the Hidden bookmarks check box to view the list of hidden bookmarks.
In the list of bookmarks, click the bookmark that you want to remove, and then click Delete.
Repeat Step 3 for each bookmark that you want to remove.
Click Close.
To work around this problem, manually remove the hidden bookmarks. To do this, follow these steps:
In Microsoft Word 2002 or in Microsoft Office Word 2003, click Bookmarks on the Insert menu.
In Microsoft Office Word 2007, click the Insert tab, and then click Bookmarks in the Links group.
Click to select the Hidden bookmarks check box to view the list of hidden bookmarks.
In the list of bookmarks, click the bookmark that you want to remove, and then click Delete.
Repeat Step 3 for each bookmark that you want to remove.
Click Close.
To work around this problem, manually remove the hidden bookmarks. To do this, follow these steps:
In Microsoft Word 2002 or in Microsoft Office Word 2003, click Bookmarks on the Insert menu.
In Microsoft Office Word 2007, click the Insert tab, and then click Bookmarks in the Links group.
Click to select the Hidden bookmarks check box to view the list of hidden bookmarks.
In the list of bookmarks, click the bookmark that you want to remove, and then click Delete.
Repeat Step 3 for each bookmark that you want to remove.
Click Close.nhjj
Click Close.
Concept:
Parabola can be defined as a plane curve generated by a point moving so that its distance from a fixed point is equal to its distance from a fixed-line.
Given:
The straight line x+y-2=0 touches a parabola at (1,1) and the focus of the parabola is the origin.
Find:
The characteristics of the parabola.
Solution:
As the straight line x+y-2=0 touches a parabola at (1,1), the straight line x+y-2=0 is a tangent to the parabola.
As the axis is a line passing through (0,0) and perpendicular to x+y-2=0.
The equation of the axis is,
x−y+λ=0
This will pass through the point (0,0),
0−0+λ=0
λ=0
So, the equation of the axis is x−y=0.
The vertex of the parabola is the point of intersection of x−y=0 and x+y=2.
Solving the equation, x = 1 and y = 1.
Hence, the coordinates of the vertex are (1,1).
Let, the coordinates of A be (x₁,y₁). Then,
(x₁+0)/2 = 1
x₁ = 2
and,
(y₁+0)/2 = 1
y₁ = 2
So, the coordinates of A are (2,2).
The directrix is a line passing through (2,2) and parallel to x+y-2=0,
The equation of the directrix is
x+y-λ=0
This will pass through the point (2,2),
2+2-λ=0
λ=4
So, the equation of the directrix is x+y-4=0.
The point (1,3) satisfies the equation x+y-4=0, so, the directrix passes through the point (1,3).
Hence, the correct option is (A) Its directrix passes through (1,3).
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